parte_6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7f0fa330",
   "metadata": {},
   "source": [
    "# 6 - Os DAGs assombrados & O Terror Causal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d8ce19a2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from videpy import Vide\n",
    "\n",
    "import networkx as nx\n",
    "# from causalgraphicalmodels import CausalGraphicalModel\n",
    "\n",
    "import stan\n",
    "import nest_asyncio\n",
    "\n",
    "plt.style.use('default')\n",
    "\n",
    "plt.rcParams['axes.facecolor'] = 'lightgray'\n",
    "\n",
    "# To DAG's\n",
    "import daft\n",
    "from causalgraphicalmodels import CausalGraphicalModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f8f700da",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To running the stan in jupyter notebook\n",
    "nest_asyncio.apply()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0036b6d",
   "metadata": {},
   "source": [
    "### RCode 6.1 - Pag 162"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8212db99",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noticiabilidade(newsworthiness): \n",
      "\n",
      " [ 0.82456357  1.85614543  0.85556981  1.4066898   1.6026727   1.42256068\n",
      "  0.71166144  1.30222516  0.56454812  3.02039213  0.93879118  1.04202561\n",
      " -0.4640972   0.12272254  1.99579665  1.59807671  1.82853378  1.15394068\n",
      "  1.48966066  1.22640255] \n",
      "\n",
      "\n",
      "Confiabilidade(trustworthiness):\n",
      "\n",
      " [ 1.24510334  1.29709756  2.10293057  0.66088341  1.76728533  0.64448519\n",
      "  1.17598088  0.35356094  1.08805257 -0.72327249  1.31462133  1.54253157\n",
      "  2.8128998   1.51862223  1.18048237  2.31948695 -0.09763283  0.87205345\n",
      "  0.74979249  0.46329186] \n",
      "\n",
      "\n",
      "Correlação:  [19.93737242]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(1914)\n",
    "\n",
    "N = 200\n",
    "p = 0.1\n",
    "\n",
    "# Não correlacionado noticiabilidade(newsworthiness) e confiabilidade(trustworthiness)\n",
    "nw = np.random.normal(0, 1, N)\n",
    "tw = np.random.normal(0, 1, N)\n",
    "\n",
    "# Selecionando os 10% melhores\n",
    "s = nw + tw  # Score total\n",
    "q = np.quantile(s, 1-p)  # Top 10% \n",
    "selected = [ True if s_i >= q else False for s_i in s ]\n",
    "print('Noticiabilidade(newsworthiness): \\n\\n', nw[selected], '\\n\\n')\n",
    "print('Confiabilidade(trustworthiness):\\n\\n', tw[selected], '\\n\\n')\n",
    "\n",
    "print('Correlação: ', np.correlate(tw[selected], nw[selected]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4b233953",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.scatter(tw, nw, s=6, color='gray')\n",
    "plt.scatter(tw[selected], nw[selected], s=7, color='blue')\n",
    "\n",
    "plt.title('Figure 6.1 - Pag162')\n",
    "plt.xlabel('Noticiabilidade ($newsworthiness$)')\n",
    "plt.ylabel('Confiabilidade ($trustworthiness$)')\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57a1c5ce",
   "metadata": {},
   "source": [
    "### RCode 6.2 - pag163\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "79a4fa5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height</th>\n",
       "      <th>leg_left</th>\n",
       "      <th>leg_right</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.463728</td>\n",
       "      <td>4.094675</td>\n",
       "      <td>4.078446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>9.854070</td>\n",
       "      <td>4.776475</td>\n",
       "      <td>4.687749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.668694</td>\n",
       "      <td>4.192607</td>\n",
       "      <td>4.256472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.523768</td>\n",
       "      <td>3.088674</td>\n",
       "      <td>3.088206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.381352</td>\n",
       "      <td>4.093217</td>\n",
       "      <td>4.048181</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     height  leg_left  leg_right\n",
       "0  8.463728  4.094675   4.078446\n",
       "1  9.854070  4.776475   4.687749\n",
       "2  8.668694  4.192607   4.256472\n",
       "3  7.523768  3.088674   3.088206\n",
       "4  9.381352  4.093217   4.048181"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 100\n",
    "\n",
    "np.random.seed(909)  # Teste com outras sementes\n",
    "\n",
    "height = np.random.normal(10, 2,  N)\n",
    "\n",
    "leg_proportion = np.random.uniform(0.4, 0.5, N)\n",
    "\n",
    "leg_left  = np.random.left = leg_proportion * height + np.random.normal(0, 0.02, N)\n",
    "leg_right = np.random.left = leg_proportion * height + np.random.normal(0, 0.02, N)\n",
    "\n",
    "\n",
    "df = pd.DataFrame({'height': height, \n",
    "                   'leg_left': leg_left, \n",
    "                   'leg_right': leg_right})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "254c1124",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O0R2i0B4i0B2i0B4ipO6OiTcygTdkRKA7RKE9RKA7RKE9RJiribeZnTSzD5rZo2b2iJl95TRfDwAAAACAWTPtxdXeJ+kj7v4OM1uQtDjl18OcarVa0UNADtEdotAeItAdotAeIqTubmoTbzM7IelrJP09SXL3HUk703o9zDd3jx4CcojuEIX2EIHuEMHd1e72ooeBHEr9njfNI95fJOmCpH9rZq+TdL+kd7l7Y/xJZna3pLsl6cyZM1pdXZUkbW1tqdvtjm5s3m631Wq1Ro+7u+r1upaWlkb3YNvc3FS5XFalUhlto9fraXFxceI2er2eNjc3L9vGwsLC6Jz/Vqsldx9tY2dnR9vb21pZWdm1jeXlZRUK/TP36/W6KpXKaBvNZlNmplqtNtrGzs6OlpeXJUndbleNRmPXNjY2NlSr1VQul0fbKBQKqlarkqTt7W212+3LtrGysiIzm7iNRqOhYrG4axudTmf0Pe50Omo2m6NtDL/Hi4uLKpVKo22USqVd3+MU+6lQKKjb7bKfZnw/zdvP08te9rLRb0PZT7O7n+bx56larer8+fPspxnfT/P281QsFuXu7KcZ30/z9PPUbDb1gte0UKiqsdXQWrn//WI/zdZ+mtefp0qlogsXLhzrfjqITWumb2ZvknSfpDe7+8fN7H2SNtz9R/f7mjvvvNPvueeeqYwH2ba6uqqNjY3oYSBn6A5RaA8R6A6ptbuu3/tMXWdvOKmPPPSM7vqSZb3h5bVDJzDAcZjGe976+vr97v6mSY9Nc3G1JyU96e4fH3z8QUlvnOLrYY7t7HCVAtKjO0ShPUSgO6RWLppuXC3p0Wcauvm6sp7e6KjDWedIJPV73tQm3u7+jKRzZnb74FNvkfTpab0e5tv29nb0EJBDdIcotIcIdIcIr39FTbdfL60uFHX2ZFnlIke7kUbq97xpr2r+fZJ+dbCi+WclfdeUXw9zamVlhdPfkBzdIQrtIQLd4Vq4uzo9XfHE2cz0125b08VLG0y6kVTq97ypTrzd/QFJE89xBwAAAJB97q6Hzm/p3KW2zp4sa32tekXXaZsZk27MvWle4w0cm16PC36QHt0hCu0hAt3hanV60rlLbV2/WNS5S+0rvk6b9hAhdXdMvJEJm5ub0UNADtEdotAeItAdjqp/7+2X7oxULprOnizrYrN7Vddp0x4ipO6OiTcyYXi/PSAlukMU2kMEusPQ3on13sceOr+lex+r68Fn+/drlqT1tareetuKXntD7Ypfj/YQIXV3TLyRCYUCqSI9ukMU2kMEuoO0/8R6aL/Tyq/lOm3aQ4TU3VE5AAAAAEmHX699raeVA3k17duJAceiXq9HDwE5RHeIQnuIQHeQXppYD1conzSxXl+r6o5T1WObdNMeIqTujiPeyIRKpRI9BOQQ3SEK7SEC3WHosOu1j/v2X7SHCKm7Y+KNTFhYWIgeAnKI7hCF9hCB7ubHQYujHUXq+2rTHiKk7o5TzQEAAIA5MVwcbXiq+PpaVWZchw1E44g3MqHZbEYPATlEd4hCe4hAd/PhsMXRZhHtIULq7ph4IxP4TS0i0B2i0B4i0N18yOKq47SHCKm741RzZEKtVlO73Y4eBnKG7hCF9hCB7ubHca86Pm20hwipu2PiDQAAAMyR/uJo0aMAMI5TzZEJOzs70UNADtEdotAeItAdotAeIqTujok3MoE3ZESgO0ShPUSgO0ShPURg4g1MsLy8HD0E5BDdIQrtIQLdIQrtIULq7ph4AwAAAFPm7mp3fd+P9/scgPnA4mrIhG63Gz0E5BDdIQrtIQLdTY+766HzWzp3qa2zJ8t6zemKHr6wPfp4fa0qSbues75Wzc1ttmgPEVJ3xxFvZEKj0YgeAnKI7hCF9hCB7qan05POXWrr+sWizl1qa6uz++NO7/LndHrRo06H9hAhdXdMvJEJXPuDCHSHKLSHCHR3vMZPGy8XTWdPlnWx2dXZk2UtLhR2fVwu2mXPyco9uI8D7SFC6u441RyZUCjwOyKkR3eIQnuIQHfHZ++p5etrVa2vVXXHqepoQr334/0+lwe0hwipu6NyAAAA4BhNOm3czHZNqPd+vN/nAMwHJt7IhI2NjeghIIfoDlFoDxHo7nBHXXU8z6eNXw3aQ4TU3THxRibUarXoISCH6A5RaA8R6O5gw9PH732srgefbcn94FuBra9V9dbbVvTaG/i+Hob2ECF1d0y8kQnlcjl6CMghukMU2kMEunvJpCPbB606PmlSzmnjR0d7iJC6OybeAAAAwMB+R7YPOn08z7cCA3A0rGqOTGg2m9FDQA7RHaLQHiLQXd/eSXR/lfH+Y/utOj6clA9XMedI95WhPURI3R0Tb2QCt5lABLpDFNpDhHnrzt3V6emKJ8EHTaL7p49P/rq83grsOMxbe8iG1N0x8UYmVKtV7ezsRA8DOUN3iEJ7iDBP3U26j7aZXfac/SbmVzOJPmhSjoPNU3vIjtTd8eslAAAAzJXDrrk+bIVyFkYDcNyYeCMTtre3o4eAHKI7RKE9RMhSd+Orjk9agfyw+2izGNpsyVJ7mB+pu+NUc2RCu92OHgJyiO4QhfYQISvdjZ9GftOJkkzSuRc7l51SftDp4iyGNluy0h7mS+ruOOKNTFheXo4eAnKI7hCF9hAhK92NH61+/IW2Pv9CZ+KR68NOF19fq+qtt63otTfUEowaB8lKe5gvqbvjiDcAAAAyY/xo9S3XL0jSVR25ZjE0ACkx8UYmdLvd6CEgh+gOUWgPEbLQ3XAl8vHTyN2d23hlXBbaw/xJ3R0Tb2RCo9GIHgJyiO4QhfYQYda7m3SLMIkj1/Ng1tvDfErdHdd4IxNWVlaih4AcojtEoT1EmPXuWIl8fs16e5hPqbtj4o1MGK5QCqREd4hCe4gw690ddoswZNest4f5lLo7TjUHAABAJhx0izAAmGVMvJEJGxsb0UNADtEdotAeImShO67nnk9ZaA/zJ3V3nGqOTKjVuMcm0qM7RKE9RKA7RKE9REjdHRNvZEK5XI4eAnKI7hCF9hCB7hCF9hAhdXdMvAEAAAAAmCIm3sgE7u+ICHSHKLSHCEftzt3V7vqUR4M84T0PEbiPNzBBschKKkiP7hCF9hBhUnd7J9nurofOb+nex+p68NmW3JmA49rxnocIqbub6sTbzD5vZg+Z2QNm9mfTfC3Mt2q1Gj0E5BDdIQrtIcLe7vZOsnu9nlpt17lLbV2/WNS5S211ekGDxVzhPQ8RUneX4nZiX+fuzyV4HQAAAByTTk+jSfYTL+yo23U9Ve+o3XM93+jq5uvK3E8bAI6I+3gjE7a3t6OHgByiO0ShPUyDu6vT076T5b3dlYumsyfLOneprTMnynpqo6PrF4t6vtHR13/xshYXuGIRx4P3PERI3d20J94u6V4zc0m/4O7vn/LrYU51Op3oISCH6A5RaA/HbXja+LlLbZ09Wdb6WlVmuyfgk7pbX6vqjlNVlYumBwstnbvU1s3XLTDpxrHiPQ8RUnc37Yn3V7v7F8xsTdJHzexRd//D8SeY2d2S7pakM2fOaHV1VZK0tbWlbrerpaUlSVK73Var1Ro97u6q1+taWloaXRi/ubmpcrmsSqUy2kav19Pi4uLEbfR6PW1ubl62jYWFBS0sLEiSWq3+wiHDbezs7Gh7e1srKyu7trG8vKxCof8foXq9rkqlMtpGs9mUmY1u0r6zs6OdnR0tLy9LkrrdrhqNxq5tbGxsqFarje4v12w2VSgURtcibG9vq91uX7aNlZWV0X9I926j0WioWCzu2kan0xl9jzudjprN5mgbw+/x4uKiSqXSaBulUmnX9zjFfioUCup2u+ynGd9P8/bzdOrUKbVaLfbTjO+nefx5qlarOn/+PPtpxvdTln6eXqw3VG8X9MYvOqXN7Z5KCwV5t7NrG8ViUe6+az8tLi6OtvH6QkGvP1PU8lKN/TSl/ZTXn6daraZGo8F+mvH9NP49nof9VKlUdOHChWPdTwexVKtRmtmPS9p095/Z7zl33nmn33PPPUnGg2xZXV3VxsZG9DCQM3SHKLSH4+bueuDplp6qd3T2ZFmvvaF22XPoDlFoDxGm0d36+vr97v6mSY9N7TwhM1sys5Xh3yW9VdLD03o9zDdOQUIEukMU2sO1Gr8N2PA08y9stPWK1ZLW1yav5Et3iEJ7iDBPp5rfIOlDg0PuJUm/5u4fmeLrYY41m83oISCH6A5RaA/XYu/13K96WUXnLrX1sqWSnt7oaH1NKk+4fS3dIQrtIULq7qZ2xNvdP+vurxv8udPdf3par4X5N7wmBEiJ7hCF9nAlxo9uSy/dBuy6WkGfv7gjs/7q5BebXZ09uf8twOgOUWgPEVJ3x+3EkAmHLVYATAPdIQrt4ah6vZ4eeHZLT290RquVl4umm06U9PFz/cUhH3luS685XRmtTr4fukMU2kOE1N1xLwhkQqpFAIFxdIcotIe99h7VHn7uk89s6aOf2dTGTldPvLCjTq//2B2nqnr5clnrL6/q3KW2um4HTrqH2wMi0B4ipO6OiTcyoV6vRw8BOUR3iEJ7+bXfBPuh81u697G6Hny2Nfo/i52e9FS9o5uvK+uJF9o6c+Kl08gXSgXdcv3hp5ePoztEoT1ESN0dE29kwvA+gEBKdIcotJdP4xPsTz7T1M7g8PXwmu3rF4s6d6k9OqpdLvav3V4pF/XW25b1xlfs7mZ9raq33rYy8dZhk9AdotAeIqTujmu8kQmlEqkiPbpDFNqbb+6uTk+XHYUeXxTt4+daevyFjm65vn/d9tmT5dEq5eNft75W3ffabTObuHr5fugOUWgPEVJ3R+UAAADXYL+J9H7PHb/V1/padbTAz/AI9ucv7kiSTi/3j3Dfcaq67wT7SifXAIAYTLyRCY1GI3oIyCG6QxTay45JE2mpf/S6VNBlE/K9p433J9MvbW84wX7kua3LjnBPe4JNd4hCe4iQujsm3siEUqmkbrcbPQzkDN0hCu1lx957Zr/qZRU9+vx2f4Vxl0pmuvm6l45sD49qTzptXHrpCPZBp5BPC90hCu0hQuruWFwNmVCpVKKHgByiO0ShvewY3jP74We39cxmR586v6UnXtjRiVpRf3FhWydrBZ271Fa7+9Jq5UdZ9Gw4SU+J7hCF9hAhdXcc8QYAALhK7q7brqvo8Rc6Or1c1FP1js6cKOvpjY5uP13Ri1s9nT1R0qPPb+86HT31pBoAEIuJNzJha2sregjIIbpDFNrLhvHru3tyPd/o6uyJom67vqL1tdroGm9Juvex+r7Xdc8KukMU2kOE1N1xqjkyget+EIHuEIX2Zpt7/7Tx8YXSSiZ97S2L+tyljn7u48/r3/1/G3J3lYsvXdd9sdmdeF33rKA7RKE9REjdHRNvZMLS0lL0EJBDdIcotBdnOKk+6PGHzm/p3sfqeuS5Ld10oqSLza5uvm5BhUJBf3FhWzcs96/v3uq89HVHua47Gt0hCu0hQuruONUcAABA+99je/w+3XtvB3bXrct69emXFkK7/XRFf3FhW7efrmhx4aXjG9xvGwDyjYk3MqHdbkcPATlEd4hCezEm3WO7VLh8Mj5+O7CF0u6TB99++4q2bl3ZNenOCrpDFNpDhNTdMfFGJrRareghIIfoDlFoL8ake2y3u37ZZPyge2wXCgUtLgQM/hjQHaLQHiKk7i57v45FLq2urkYPATlEd4hCe2mNX9e991rsSQujRdxjOwW6QxTaQ4TU3XHEGwAA5Nak67r3TqoPOsINAMBRcMQbmeC+/wqzwLTQHaLQXjp7r+se3nd73Lwe4d6L7hCF9hAhdXdMvJEJ9Xo9egjIIbpDFNo7usNu/3WYrNxjOwW6QxTaQ4TU3THxRiZwf0dEoDtEob2jGb+n9oPPtq766EUW7rGdAt0hCu0hQurumHgjE4pFbn6K9OgOUWjvcO6uVnv3iuPt7tUd/c7LqeSHoTtEoT1ESN0di6sBAIBMGV8Qrd1zPbfZ0ZkTJT36/PauRdLMmEwDAGbDoUe8zeyfHeVzwDRtbm5GDwE5RHeIQnsHG18QrSjXy1fK+sKLXd33RFPX1Qr7LpKGg9EdotAeIqTu7iinmt814XPfeNwDAQ5SLpejh4AcojtEob2DjS+IduPJBZ1vdHR6uX/K4HMNFkm7WnSHKLSHCKm72/dUczP7B5K+R9KtZvbg2EMrkv5k2gMDxlUqFW1vb0cPAzlDd4hCe4cbv7f2g4WWzl1q66+eremO0zUm3VeJ7hCF9hAhdXcHXeP9oKRvlvRPJf3jsc/X3f3iVEcFAABwgP6CaP2/j0/CAQCYRQdNvP+Fu3+ZmX2puz+ebETABFtbW9FDQA7RHaLMQ3vurk5PSSbD45NwXL156A7ZRHuIkLq7gybebTN7v6Qbzexf7H3Q3b9/esMCduv1WCUH6dEdomS9vfFVx8dXGE85GceVy3p3yC7aQ4TU3R20uNrbJP2+pC1J90/4AySzuLgYPQTkEN0hStbbG191fLjC+HAyfu9jdT34bEvuV36/bUxX1rtDdtEeIqTubt8j3u7+nKQPmNkj7v7JhGMCAAAZNlx1fHjEu1w0tbu+azLevyY7eqQAAKRxlNuJtczsP5jZw5JkZq81sx+Z8riAXdrtdvQQkEN0hyhZaM/d1e7uf9R6fa2qt962otfeUJO0+xZg3O5rNmWhO8wn2kOE1N0dZeL9ryX9kKS2JLn7g5LeOc1BAXu1Wq3oISCH6A5RZr29o5w23l/wbPfkeu9kHLNl1rvD/KI9REjd3VEm3ovu/qd7PteZxmCA/ayurkYPATlEd4gy6+0Nr+G+rlbQ5y/uqHOE9WlYWG32zXp3mF+0hwipuzvKxPs5M7tVkkuSmb1D0tNTHRUAAAix3ynk458vF003nSjp4We39cxmR488t3XgYmksrAYAyLuDbic29L2S3i/pVWb2BUmfk/TtUx0VsAe3mUAEukOUqPYOug3Y3s/fcaqqx1/o6PTy4Yul7V3lnIXVZhPveYhCe4gwS7cTkyS5+2fd/RsknZb0Knf/akn/+dRHBozZ3NyMHgJyiO4QJaq9SbcBG37+iRfaOlEtjD6/UCroluuPtlgaC6tlA+95iEJ7iJC6u6Ocai5JcveGu9cHH75nSuMBJlpaWooeAnKI7hAldXvD08jHJ8g3nXjppLhSQeq4608eb6rd7Y1OFb+SxdJYWG328Z6HKLSHCKm7O/LEew9+VY2kikXOSUR6dIcoKdvbe/31a05XdNetyzKz0efaXVfJpK+6uabzja4+8pn+56WjL5Y2aZVzzBbe8xCF9hAhdXdXO/FmVRQAAObA3tPLu24ys12fMzPdfN2CXmj1//N/erm061R0AABwsH0XVzOzuiZPsE0S54khKa79QQS6Q5Tjbu+gW3kNTy8fLpw2fM7ezw0XVHvkua3Lnov5wHseotAeIqTubt+Jt7uvpBwIcJCFhQVtbW1FDwM5Q3eIclB7V3o/7EkrkkvatY3hpHp8m3s/1z9VfPJzMR94z0MU2kOE1N1d7anmQFILCwvRQ0AO0R2i7Nfe1dwPe++p5O3u5duYdP31ftdkc632/OI9D1FoDxFSd8fEGwCAjGh3XZ+/uPt2X8MVyfez91Zee6/f5jptAACmb99TzYFZ0mq1ooeAHKI7RJnUnrvr0ee39cxmW0/Xd/RXbqqpVNBlp5GbXX40eu/p4ZOu6QZ4z0MU2kOE1N0x8UYmHOV0SuC40R1SGr92e1J7w1PG71xb0EPPbOvJF7sytfSFjbZettRfZbw/ub5828Prs4e4ThuT8J6HKLSHCKm7O/RUczOrm9nGnj/nzOxDZvbFR/j6opn9uZl9+HiGjDxaXFyMHgJyiO6Qyt5rt2u1y28eMjxl/PlmT4WC6fRyUU/VO3rFakkXNjtXdPSa67QxCe95iEJ7iJC6u6Mc8X6vpCcl/Zr6txJ7p6RbJX1C0r+R9LWHfP27JD0iafVqBwkAwDy7/F7ak5+395ZeN50oabDmuCSNFkoDAACz5SiLq73d3X/B3evuvuHu75f0n7n7PZKuO+gLzewmSd8k6RePYazIsZ2dneghIIfoDqnsXQCt12lPfN7wSPX6WlVvvW1Frz5d07kXOzq9zEJpuHa85yEK7SFC6u6OcsS7aWZ/W9IHBx+/Q9LwhmeHnRj/Xkn/SBL3BMc12d7ejh4CcojukNL6WlW3X7+grtuh7Y1fs81CaTguvOchCu0hQurujjLx/nZJ75P08+pPtO+T9B1mVpP0P+z3RWb2Nknn3f1+M/vaA553t6S7JenMmTNaXe2fkb61taVut6ulpSVJUrvdVqvVGj3u7qrX61paWlKx2P9/H5ubmyqXy6pUKqNt9Hq90fn7e7fR6/W0ubl52TYWFhZG93Vrtfr3OB1uY2dnR9vb21pZWdm1jeXlZRUK/RMI6vW6KpXKaBvNZlNmNrpmb2dnRzs7O1peXpYkdbtdNRqNXdvY2NhQrVZTuVwebaNQKKharUrqh9Juty/bxsrKyug0w73baDQaKhaLu7bR6XRG3+NOp6NmsznaxvB7vLi4qFKpNNpGqVTa9T1OsZ8KhYK63S77acb307z9PK2trY1WvGQ/ze5+ytrPk7trs7mlovmu/dRoNPTZ1oKe2ujojTevaHHnBV1/cvXQ/fTm29bUdanXabOf+Hm6pv1ULBZ3Xa7AfprN/TSPP0+1Wk2NRoP9NOP7afx7PA/7qVKp6MKFC8e6nw5i01rNzcz+F0nfKakjqar+Nd6/7e7fsd/X3HnnnX7PPfdMZTzIttXVVW1sbEQPAzlDdzhuw0XUnnihrRtXS3rdy6vqev/08eZOT//bfc/phuWirj95Ut3Wpm49tbDvLcKA48Z7HqLQHiJMo7v19fX73f1Nkx47yqrmX2pm/8HMHh58/Foz+5HDvs7df8jdb3L3W9RfkO33D5p0Awfp9bhwEenRHY5bpyc98UJb9XZXv/eZTX3okQ393mc2+iuZl023n67o6XpXpp5evlrium0kxXseotAeIqTu7iiLq/1rST8kqS1J7v6g+hNpIJnNzc3oISCH6A5H5e5qD5YiH//73o/LRdONqyU98UL/muzHnt/RidpLC6O9/fYVvesrT+mVS53RQmtct41UeM9DFNpDhNTdHeUa70V3/9M9p7l1ruRF3P0PJP3BlXwNMG55eZk3ZSRHdziK4enj5y61dfZESS7pyRf799V+zemKHr6wPVr8bH2tqte/oiY36emNjpYWCtrY6o1NsE2LC9JXfvEp3bGxyaQbSfGehyi0hwipuzvKxPs5M7tVgxXMzewdkp6e6qiAPYaLJgAp0R2OYvwe3J9/oSPJdXq5f5r4bddVdt2f+45TVZWLpje8vKb1NalU6H/93gl2sVhk0o3keM9DFNpDhNTdHWXi/b2S3i/pVWb2BUmfU3+lcwAAcm94D+5zl9q65fr+KqjDI9yLC4WJt/savx3Y8H8BAMD8OnTi7e6flfQNZrYkqeDudTN7t/r36AaSqNfr0UNADtEdjmp9rTo6mu3uo7/vfeyoaA8R6A5RaA8RUnd35OPr7t5w9+Ho3jOl8QATDe8tCKREdziq/hFsu+zvkz4+CtpDBLpDFNpDhNTdXe2J7Vx4hqQWFhaih4AcojsM7V2pfNpoDxHoDlFoDxFSd3eUa7wnSff/PgAACLRr1fLByuR77vQBAABwoH0n3mZW1+QJtkmqTW1EwATNZjN6CMghuoO0e9Xyl1Ymn+5r0h4i0B2i0B4ipO5u34m3u6+kHAhwEI4uIQLdZZ+7T7xd15UYX7V8fGXyaaI9RKA7RKE9REjd3dWeag4kVavV1G63o4eBnKG7bDvOU8SvZmXya0F7iEB3iEJ7iJC6O+5WDwCYS3tPEW93r36BtKtZmRwAAGCIiTcyYWdnJ3oIyCG6y45Jq44PTxG/2Ozq7ImSHn1+W/c+VteDz7bkPttrhNIeItAdotAeIqTujlPNkQm8ISMC3WXDQaeUD08Rl6R7H6snXSDtWtAeItAdotAeIqTujiPeyITl5eXoISCH6C4b9p5S3um99NjwFPFdR78TLZB2LWgPEegOUWgPEVJ3xxFvAEAmja9YfpRVx1MvkAYAADDExBuZ0O12o4eAHKK72dXr9fTJZ7b0VL2jsyfLes3pyqGT6v7R74SDvAa0hwh0hyi0hwipu+NUc2RCo9GIHgJyiO7SmrRA2n7Pe+DZLd372KY2drp64oW2uj5fq47THiLQHaLQHiKk7o6JNzKBa38Qge7SGS6QdpRVxzs96emNjm6+rqwnXmjrxtXSXE26JdpDDLpDFNpDhNTdMfFGJhQKpIr06C6dgxZI22t4TfdKuaC7vmRZbzizmG6gidAeItAdotAeIqTujmu8AQDhjrpA2hALpQEAgCxh4o1M2NjYiB4Ccojurtz4SuNX6kom01laKO1q0B4i0B2i0B4ipO6O8zqQCbVaLXoIyCG6uzJXcp32JMN7boP2EIPuEIX2ECF1d0y8kQnlcjl6CMghursyV3KdNg5Ge4hAd4hCe4iQujsm3gCAYzG8Tvtis3uk67QBAADygmu8kQnNZjN6CMghurtyLHp2PGgPEegOUWgPEVJ3x8QbmcBtJhCB7q7cvC96lgrtIQLdIQrtIULq7qgcmVCtVqOHgByiO0ShPUSgO0ShPURI3R0TbwDIEXdXu3tlq40DAADg2nCqOTJhe3s7egjIoXnrbni7r3OX2jp7sqz1tarM7LLnXO19uHF85q09ZAPdIQrtIULq7jjijUxot9vRQ0AOzVt3h93u61rvw43jM2/tIRvoDlFoDxFSd8fEG5mwvLwcPQTk0Lx1d9jtvrgP9+yYt/aQDXSHKLSHCKm741RzAMiRg273NZyYD09F53RzAACA48HEG5nQ7Xajh4AcmsfuDrvdF/fhng3z2B5mH90hCu0hQurumHgjExqNRvQQkEN57I77cM+GPLaHeHSHKLSHCKm74xpvZMLKykr0EJBDdIcotIcIdIcotIcIqbtj4o1M2HvLIyAFukMU2kMEukMU2kOE1N0x8QaAGeTuane5nRcAAMA84BpvZMLGxkb0EJBDUd0N76c9XF18fa3K0YCc4T0PEegOUWgPEVJ3xxFvZEKtVoseAnIoqjvupw3e8xCB7hCF9hAhdXdMvJEJ5XI5egjIoajuhvfTvtjscj/tnOI9DxHoDlFoDxFSd8ep5gCQmLur09OBE2rupw0AADA/mHgjE7i/IyIcZ3fDyXapoCNdv839tPON9zxEoDtEoT1E4D7ewATFIjMQpHdc3Q0XS7v3sboeeLqlJ17Y4fptHIj3PESgO0ShPURI3R0Tb2RCtVqNHgJy6Li6G18s7al6R2dOcP02DsZ7HiLQHaLQHiKk7o5TzQHgGuy9XnvS9dvDxdLGTy9fXzv4Gm8AAADMDybeyITt7e3oISCHDutu7/22X3O6oocvbE+8fnvvYmlcv42D8J6HCHSHKLSHCKm741RzZEKn04keAnLosO723m97q7P//bf7i6VxhBtHw3seItAdotAeIqTubmoTbzOrmtmfmtknzexTZvYT03otzL+lpaXoISCHDutu7/22FxcK3H8bx4L3PESgO0ShPURI3d00TzXflvT17r5pZmVJf2xm/7e73zfF1wSApPaeQs79twEAALDX1Cbe7u6SNgcflgd/fFqvh/nGKUiIcJTu9t5vm/tv4zjwnocIdIcotIcIc3OquSSZWdHMHpB0XtJH3f3j03w9zK9msxk9BOQQ3SEK7SEC3SEK7SFC6u6muqq5u3clvd7MTkr6kJm9xt0fHn+Omd0t6W5JOnPmjFZXVyVJW1tb6na7o3Pv2+22Wq3W6HF3V71e19LS0ujm55ubmyqXy6pUKqNt9Ho9LS4uTtxGr9fT5ubmZdtYWFjQwsKCJKnVasndR9vY2dnR9va2VlZWdm1jeXlZhUL/9xj1el2VSmW0jWazKTNTrVYbbWNnZ0fLy8uSpG63q0ajsWsbGxsbqtVqKpfLo20UCoXR/ea2t7fVbrcv28bKyspoFeW922g0GioWi7u20el0Rt/jTqejZrM52sbwe7y4uKhSqTTaRqlU2vU9TrGfzEy9Xo/9NOP7ad5+ntbW1rS1tcV+mvH9NI8/T5VKRRcuXGA/zfh+mrefp+HXsp9mez/N489TtVpVs9lkP834fhr/Hs/DflpYWNBzzz13rPvpINY/I3z6zOzHJDXd/Wf2e86dd97p99xzT5LxIFtWV1e1sbERPQzkDN0hCu0hAt0hCu0hwjS6W19fv9/d3zTpsWmuan56cKRbZlaTdJekR6f1ephvqX5BBIyjO0ShPUSgO0ShPURI3d00TzV/haRfNrOi+hP833D3D0/x9TDH6vV69BCQQ3SHKLSHCHSHKLSHCKm7m+aq5g9KesO0to98WVxcZOENXDF3V6enq761F90hCu0hAt0hCu0hQuruprq4GnBchotIAEedTLu7Hjq/pXOX2jp7sqz1teqhi17sRXeIQnuIQHeIQnuIkLq7qd5ODACO03Ayfe9jdT34bOvAa3M6PencpbauXyzq3KW2Or2EAwUAAADGMPFGJjQajeghYAZcyWS6XDSdPVnWxWZXZ0+Wr+p0c7pDFNpDBLpDFNpDhNTdcV4HMqFUKqnb7UYPA8GGk+nh6eOHTabX16q641T1qq/xpjtEoT1EoDtEoT1ESN0dR7yRCZVKJXoImBHra1W99bYVvfaG2qHPNbOrnnRLdIc4tIcIdIcotIcIqbvjiDeATOlPpqNHAQAAABwdR7yRCVtbW9FDQA7RHaLQHiLQHaLQHiKk7o6JNzKB634Qge4QhfYQge4QhfYQIXV3TLyRCUtLS9FDQA7RHaLQHiLQHaLQHiKk7o6JNwAAAAAAU8TEG5nQbrejh4AcojtEoT1EoDtEoT1ESN0dE29kQqvVih4CcojuEIX2EIHuEIX2ECF1d0y8kQmrq6vRQ0AO0R2i0B4i0B2i0B4ipO6OiTcAAAAAAFPExBuZ4O7RQ0AO0R2i0B4i0B2i0B4ipO6OiTcyoV6vRw8BOUR3iEJ7iEB3iEJ7iJC6OybeyATu74gIdIcotIcIdIcotIcI3McbmKBYLEYPATlEd4hCe4hAd4hCe4iQujsm3gAAAAAATBETb2TC5uZm9BCQQ3SHKLSHCHSHKLSHCKm7Y+KNTCiXy9FDQA7RHaLQHiLQHaLQHiKk7o6JNzKhUqlEDwE5RHeIQnuIQHeIQnuIkLo7Jt4AAAAAAEwRE29kwtbWVvQQkEN0hyi0hwh0hyi0hwipu2PijUzo9XrRQ0AO0R2i0B4i0B2i0B4ipO6OiTcyYXFxMXoIyCG6QxTaQwS6QxTaQ4TU3THxBgAAAABgiph4IxPa7Xb0EJBDdIcotIcIdIcotIcIqbtj4o1MaLVa0UNADtEdotAeItAdotAeIqTujok3MmF1dTV6CMghukMU2kMEukMU2kOE1N0x8QYAAAAAYIqYeCMTuM0EItAdotAeItAdotAeInA7MWCCzc3N6CEgh+gOUWgPEegOUWgPEVJ3x8QbmbC0tBQ9BOQQ3SEK7SEC3SEK7SFC6u6YeCMTisVi9BCQQ3SHKLSHCHSHKLSHCKm7Y+INAAAAAMAUMfFGJnDtDyLQHaLQHiLQHaLQHiJwjTcwwcLCQvQQkEN0hyi0hwh0hyi0hwipu2PijUzgDRkR6A5RaA8R6A5RaA8RmHgDAAAAADBHmHgjE1qtVvQQkEN0hyi0hwh0hyi0hwipu2PijUxw9+ghIIfoDlFoDxHoDlFoDxFSd8fEG5mwuLgYPQTkEN0hCu0hAt0hCu0hQurumHgDAAAAADBFTLyRCTs7O9FDQA7RHaLQHiLQHaLQHiKk7o6JNzJhe3s7egjIIbpDFNpDBLpDFNpDhNTdTW3ibWZnzexjZvZpM/uUmb1rWq+F+beyshI9BOQQ3SEK7SEC3SEK7SFC6u5KU9x2R9IPuPsnzGxF0v1m9lF3//QUXxMAAAAAgJkytSPe7v60u39i8Pe6pEck3Tit18N86/V60UNADtEdotAeItAdotAeIqTuLsk13mZ2i6Q3SPp4itfD/Nnc3IweAnKI7hCF9hCB7hCF9hAhdXfTPNVckmRmy5J+S9K73X1jwuN3S7pbks6cOaPV1VVJ0tbWlrrdrpaWliRJ7XZbrVZr9Li7q16va2lpScViUVL/m1cul1WpVEbb6PV6o3u07d1Gr9fT5ubmZdtYWFjQwsKCJKnVasndR9vY2dnR9vb26JqA4TaWl5dVKPR/j1Gv11WpVEbbaDabMjPVarXRNnZ2drS8vCxJ6na7ajQau7axsbGhWq2mcrk82kahUFC1WpXUXwyg3W5fto2VlRWZ2cRtNBoNFYvFXdvodDqj73Gn01Gz2RxtY/g9XlxcVKlUGm2jVCrt+h6n2E/DbbGfZns/zdvP0+nTp0cLb7CfZnc/zePPU6VS0YULF9hPM76f5u3nycxGf9hPs7uf5vHnqVqtqtlssp9mfD+Nf4/nYT8tLCzoueeeO9b9dBBz9wOfcC3MrCzpw5J+z91/9rDn33nnnX7PPfdMbTzIrtXVVW1sXPZ7G2Cq6A5RaA8R6A5RaA8RptHd+vr6/e7+pkmPTXNVc5P0S5IeOcqkGwAAAACAeTTNa7zfLOk7JX29mT0w+PM3p/h6mGP1ej16CMghukMU2kMEukMU2kOE1N1N7Rpvd/9jSQef6A4cUaVS0dbWVvQwkDN0hyi0hwh0hyi0hwipu0uyqjlwrYYLLQAp0R2i0B4i0B2i0B4ipO6OiTcAAAAAAFPExBuZ0Gw2o4eAHKI7RKE9RKA7RKE9REjdHRNvZMJh98UDpoHuEIX2EIHuEIX2ECF1d0y8kQm1Wi16CMghukMU2kMEukMU2kOE1N0x8QYAAAAAYIqYeCMTdnZ2ooeAHKI7RKE9RKA7RKE9REjdHRNvZAJvyIhAd4hCe4hAd4hCe4jAxBuYYHl5OXoIyCG6QxTaQwS6QxTaQ4TU3THxBgAAAABgiph4IxO63W70EJBDdIcotIcIdIcotIcIqbtj4o1MaDQa0UNADtEdotAeItAdotAeIqTujok3MoFrfxCB7hCF9hCB7hCF9hCBa7yBCQoFUkV6dIcotIcIdIcotIcIqbujcgAAAAAApoiJNzJhY2MjegjIIbpDFNpDBLpDFNpDhNTdMfFGJtRqteghIIfoDlFoDxHoDlFoDxFSd8fEG5lQLpejh4AcojtEoT1EoDtEoT1ESN0dE28AAAAAAKaIiTcyodlsRg8BOUR3iEJ7iEB3iEJ7iJC6OybeyARuM4EIdIcotIcIdIcotIcI3E4MmKBarUYPATlEd4hCe4hAd4hCe4iQujsm3gAAAAAATBET76vg7mp3PXoYubK9vR09BOQQ3SEK7SEC3SEK7SFC6u5KSV9tDri7Hjq/pXOX2jp7sqz1tarMLHpYc6/dbkcPATlEd4hCe4hAd4hCe4iQujuOeF+hTk86d6mt6xeLOneprU4vekT5sLy8HD0E5BDdIQrtIQLdIQrtIULq7ph4X6Fy0XT2ZFkXm12dPVlWucjRbgAAAADA/jjV/Cqsr1V1x6kqk+6Eut1u9BCQQ3SHKLSHCHSHKLSHCKm7Y+J9FcxM5WL0KPKl0WhEDwE5RHeIQnuIQHeIQnuIkLo7TjVHJqysrEQPATlEd4hCe4hAd4hCe4iQujsm3sgEVo5HBLpDFNpDBLpDFNpDhNTdMfEGAAAAAGCKmHgjEzY2NqKHgByiO0ShPUSgO0ShPURI3R0Tb2RCrVaLHgJyiO4QhfYQge4QhfYQIXV3TLyRCeVyOXoIyCG6QxTaQwS6QxTaQ4TU3THxBgAAAABgiph4IxO4vyMi0B2i0B4i0B2i0B4icB9vYIJisRg9BOQQ3SEK7SEC3SEK7SFC6u6YeCMTqtVq9BCQQ3SHKLSHCHSHKLSHCKm7Y+INAAAAAMAUmbtHj2HEzC5Iejx6HJhJpyQ9Fz0I5A7dIQrtIQLdIQrtIcI0unulu5+e9MBMTbyB/ZjZn7n7m6LHgXyhO0ShPUSgO0ShPURI3R2nmgMAAAAAMEVMvAEAAAAAmCIm3siK90cPALlEd4hCe4hAd4hCe4iQtDuu8QYAAAAAYIo44g0AAAAAwBQx8cbMMrOzZvYxM/u0mX3KzN4VPSbkg5lVzexPzeyTg/Z+InpMyA8zK5rZn5vZh6PHgvwws8+b2UNm9oCZ/Vn0eJAPZnbSzD5oZo+a2SNm9pXRY8L8M7PbB+91wz8bZvbuqb8up5pjVpnZKyS9wt0/YWYrku6X9K3u/ungoWHOmZlJWnL3TTMrS/pjSe9y9/uCh4YcMLP3SHqTpFV3f1v0eJAPZvZ5SW9yd+6ljGTM7Jcl/ZG7/6KZLUhadPdLwcNCjphZUdIXJH2Fuz8+zdfiiDdmlrs/7e6fGPy9LukRSTfGjgp54H2bgw/Lgz/8lhJTZ2Y3SfomSb8YPRYAmCYzOyHpayT9kiS5+w6TbgR4i6S/nPakW2LijYwws1skvUHSx4OHgpwYnO77gKTzkj7q7rSHFN4r6R9J6gWPA/njku41s/vN7O7owSAXvkjSBUn/dnB5zS+a2VL0oJA775T06yleiIk3Zp6ZLUv6LUnvdveN6PEgH9y96+6vl3STpC83s9cEDwlzzszeJum8u98fPRbk0le7+xslfaOk7zWzr4keEOZeSdIbJf1Ld3+DpIakH4wdEvJkcHnD2yX9ZorXY+KNmTa4vva3JP2qu/929HiQP4PT3j4m6W8EDwXz782S3j641vYDkr7ezH4ldkjIC3f/wuB/z0v6kKQvjx0RcuBJSU+OnVH2QfUn4kAq3yjpE+7+bIoXY+KNmTVY4OqXJD3i7j8bPR7kh5mdNrOTg7/XJN0l6dHQQWHuufsPuftN7n6L+qe+/b67f0fwsJADZrY0WMRUg1N93yrp4dhRYd65+zOSzpnZ7YNPvUUSC+gipW9TotPMpf4pHsCserOk75T00OBaW0n6J+7+f8UNCTnxCkm/PFjpsiDpN9ydWzsBmFc3SPpQ//fdKkn6NXf/SOyQkBPfJ+lXB6f8flbSdwWPBzkx+CXjXZL++2Svye3EAAAAAACYHk41BwAAAABgiph4AwAAAAAwRUy8AQAAAACYIibeAAAAAABMERNvAAAAAACmiIk3AAAzxMw2p7DNrpk9YGYPm9nvjt2n/oyZffBqx2Rm32pmrz7m4QIAMHeYeAMAMP9a7v56d3+NpIuSvleS3P0pd3/HNWz3WyUx8QYA4BBMvAEAmHFmdquZfcTM7jezPzKzV419/j4ze8jMfuqIR8v/k6QbB19/i5k9PPj7opn9hpl92sw+ZGYfN7M3jY3hp83sk4PXu8HMvkrS2yX988HR9FuP/18OAMB8YOINAMDse7+k73P3L5P0P0n6+cHn3yfpfe6+LunJwzZiZkVJb5H0OxMe/h5JL7j7qyX9qKQvG3tsSdJ97v46SX8o6b9z9/842M4/HBxN/8ur+6cBADD/mHgDADDDzGxZ0ldJ+k0ze0DSL0h6xeDhr5T0m4O//9oBm6kNvvYZSTdI+uiE53y1pA9Ikrs/LOnBscd2JH148Pf7Jd1yhf8MAAByjYk3AACzrSDp0uCo8vDPHVe4jZa7v17SKyWZBtd4X4G2u/vg711JpSv8egAAco2JNwAAM8zdNyR9zsz+liRZ3+sGD98n6b8c/P2dR9hWU9L3S/oBM9s7ef4TSX978BqvlrR+hOHVJa0c4XkAAOQaE28AAGbLopk9OfbnPZK+XdLfN7NPSvqUpG8ZPPfdkt5jZg9Kuk3Si4dt3N3/XP3TyL9tz0M/L+m0mX1a0k8NXuew7X1A0j80sz9ncTUAAPZnL505BgAAssTMFtU/jdzN7J2Svs3dv+Wwr9tnW0VJZXffGkyi/72k29195xiHDABALnGNFgAA2fVlkn7OzEzSJUn/zTVsa1HSx8ysrP514N/DpBsAgOPBEW8AAAAAAKaIa7wBAAAAAJgiJt4AAAAAAEwRE28AAAAAAKaIiTcAAAAAAFPExBsAAAAAgCli4g0AAAAAwBT9/7AXmO6IGjImAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.scatter(leg_right, leg_left, s=5, alpha=0.3)\n",
    "\n",
    "plt.title('Dados dos legs')\n",
    "plt.xlabel('Leg Right')\n",
    "plt.ylabel('Leg Left')\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c7175e74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "plt.hist(df.height, rwidth=0.9, density=True)\n",
    "plt.grid(ls='--', color='white', alpha=0.4)\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(17, 6))\n",
    "plt.hist(df.leg_left, rwidth=0.9, density=True, alpha=0.5)\n",
    "plt.hist(df.leg_right, rwidth=0.9, density=True, alpha=0.5)\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d5941242",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning in '/tmp/httpstan_724orym0/model_fow2wtab.stan', line 17, column 27: Argument\n",
      "    100 suggests there may be parameters that are not unit scale; consider\n",
      "    rescaling with a multiplier (see manual section 22.12).\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   1% (100/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   2% (200/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   4% (300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   5% (400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   6% (500/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   8% (600/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   9% (700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  11% (900/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  14% (1100/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  16% (1300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  19% (1500/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  20% (1600/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  21% (1700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  22% (1800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  24% (1900/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  26% (2100/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  28% (2200/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  30% (2400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  32% (2600/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  35% (2800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  38% (3000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  39% (3100/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  41% (3300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  42% (3400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  58% (4600/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  72% (5800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  86% (6900/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 3.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 3.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.32 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_39c5vric/model_fow2wtab.stan', line 22, column 8 to column 86)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 4e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.4 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int<lower=0> N;\n",
    "        vector[N] height;\n",
    "        vector[N] leg_left;\n",
    "        vector[N] leg_right;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real beta_left;\n",
    "        real beta_right;\n",
    "        real<lower=0> sigma; \n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        alpha ~ normal(10, 100);\n",
    "        beta_left ~ normal(2, 10);\n",
    "        beta_right ~ normal(2, 10);\n",
    "        sigma ~ exponential(1);\n",
    "        \n",
    "        height ~ normal(alpha + beta_left * leg_left + beta_right * leg_right, sigma);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'height': height,\n",
    "    'leg_left': leg_left,\n",
    "    'leg_right': leg_right\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)\n",
    "\n",
    "alpha = samples['alpha'].flatten()\n",
    "beta_left = samples['beta_left'].flatten()\n",
    "beta_right = samples['beta_right'].flatten()\n",
    "sigma = samples['sigma'].flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c7fb431",
   "metadata": {},
   "source": [
    "### RCode 6.4 - pag164"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "31bd1301",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.94</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.34</td>\n",
       "      <td>1.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_left</th>\n",
       "      <td>-1.52</td>\n",
       "      <td>2.04</td>\n",
       "      <td>-5.03</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_right</th>\n",
       "      <td>3.52</td>\n",
       "      <td>2.03</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>7.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.66</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean   std  7.0%  93.0%\n",
       "alpha       0.94  0.34  0.34   1.54\n",
       "beta_left  -1.52  2.04 -5.03   2.40\n",
       "beta_right  3.52  2.03 -0.30   7.06\n",
       "sigma       0.66  0.05  0.58   0.75"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e44280e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Leg right & Leg left')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1954153",
   "metadata": {},
   "source": [
    "### RCode 6.5 - pag164"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "06d140e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.scatter(beta_right, beta_left, s=5, alpha=0.3)\n",
    "\n",
    "plt.title('Posteriori Beta legs')\n",
    "plt.xlabel('Beta Right')\n",
    "plt.ylabel('Beta Left')\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e67bc4c5",
   "metadata": {},
   "source": [
    "### RCode 6.6 - pag 165"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "89ba1e67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v75ckNRoNVSqV89oYHR1VsVhUNpvttNHT06NCoSBJqtVqqtfrF7QxMDDQuXDE7DYqlYoymcx5bUxNTXVe46mpKY2Pj3famH6N+/r61Nvb22mjt7f3vNd4JfZTsVjUyZMn6adl3k/S6nw/DQwMqFqt0k/LoJ92banqwNGzuvv6QfWYqRmCHnl+WLu2rNXavpySJFmwn24eGtfBY+d0z45Nrb5vNvXooRHt2bpOA4WskiRRKTeswSSvq9e1nnNouKxavaGdQ2slScPlCT1/sqy7tg+2Xq9GU48fHtHea9arlO9VkiQqZE9qaG1RQ2tb/fLsiVE1m0E3bV4jSSoUCspmenTHdRtb/Vif0hNHTuvWbetVzLbayGZO6BtfebWOtyffB4+fU0+Pdc77LhQKKmQzum3bhtbrV5vSky+e1u3XbVQu8+Xv6m98WaLBgdZr+syxs8pnM9o+2MpHPp9XKdervdeub2Vjoq6nXzqjO7dvVG/Pl9u4eWiNNpRar+mBo2dUymf18o2tvn3xVKvfGPdW1vupm37q6elRtVqln5Z5P63W91OxWNSpU6fop2XeT9Ov8Ursp/lYCGHeBRaLmb1b0lgI4Rcvtswtt9wS9u3btyT1IG5Jkmh0dNS7DESK/C0fi3HedDdtLLTMQrppY6Flph+/d8cmPfTcydTXcyVtTC+zGDg3fnlh/IMn8oe07d69+4kQwm1zPZbaoeZmVjKzgel/S/paSQfSWh9wKRqNhncJiBj5g6dKbcq7BESM8Q+eyB88pXmo+VWS/rq9y71X0p+EEP4+xfUBXatUKt4lIGLkD56efPG0dwmIGOMfPJE/eEptj3cI4XAIYU/7zy0hhJ9Ja13ApZo+twPwQP7g6fb2OeCAB8Y/eCJ/8MTtxBClnh6iDz/kD55mXiQNWGqMf/BE/uCJ9AEAAAAAkCIm3ogSV7SEJ/IHTx8/NOxdAiLG+AdP5A+emHgjStP3BAQ8kD94un7TgHcJiBjjHzyRP3hi4o0oZbNZ7xIQMfIHT4MDBe8SEDHGP3gif/CU5u3EAABw88D+4/M+/uB9m5eoEgAAEDv2eCNK4+Pj3iUgYuQPnp45dta7BESM8Q+eyB88MfFGlLidBDyRP3jKZzPeJSBijH/wRP7gifQhSoUC5zjCD/mDp+2DXFwNfhj/4In8wRMTbwAAAAAAUsTF1RClWq3mXQIiRv7g6YtnKt4ldIWL461OjH/wRP7giT3eiFK9XvcuAREjf/A0PMqGJ/ww/sET+YMn9ngjSv39/RodHfUuA5EifwtbTns756tlJe513Xvtej303EnvMhApxj94In/wxB5vAAAAAABSxMQbUWo0Gt4lIGLkD57KExxqCT+Mf/BE/uCJiTeiVKmsjIsLYXUif/D09EtnvEtAxBj/4In8wRMTb0RpYID72MIP+YOnO7dv9C4BEWP8gyfyB09MvBElM/MuAREjf/DU28NHP/ww/sET+YMnPn0BAAAAAEgRtxNDlLiVBDyRP3h6mFuJnWel3LpOWpm3r5uN8Q+eyB88sccbUSoWi94lIGLkD55uGlrjXQIixvgHT+QPnph4I0rZbNa7BESM/MHThlLeuwREjPEPnsgfPDHxBgAAAAAgRZzjjShxH0d4Wu35m+881dVwjupKd+Ao9/GGn9U+/mF5I3/wxB5vRCmTyXiXgIiRP3gq5TnUEn4Y/+CJ/METE29EqVAoeJeAiJE/eHr5xn7vEhAxxj94In/wxMQbAAAAAIAUMfFGlGq1mncJiBj5g6cXT3GOI/ww/sET+YMnJt6I0tTUlHcJiBj5g6cz42x4wg/jHzyRP3hi4o0olUol7xIQMfIHT3u2rvcuARFj/IMn8gdPTLwBAAAAAEgRE29EiUON4In8wdPZ8UnvEhAxxj94In/wxMQbURofH/cuAREjf/B04OhZ7xIQMcY/eCJ/8MTEG1EaGBjwLgERI3/wdPf1g94lIGKMf/BE/uCJiTeiZGbeJSBi5A+eesgfHDH+wRP5gycm3ohSCMG7BESM/MFTk/zBEeMfPJE/eGLijSiVy2XvEhAx8gdPjzw/7F0CIsb4B0/kD556vQsAPPT19XGBDbghf/C0a8taLrDm4IH9x+d9/MH7Ni9RJb4Y/+CJ/METe7wRpd5evnOCH/IHT2v7ct4lIGKMf/BE/uCJ9AEAltRi7fmbr51Y9h7Gjr3IAICVIvU93maWMbMnzewDaa8L6FalUvEuAREjf/D09EunvUtAxBj/4In8wdNSHGr+Q5I+twTrAbrGoUbwRP7gaV1f3rsERIzxD57IHzylOvE2s6slfYOk30lzPcClyufZ8IQf8gdP12woeZeAiDH+wRP5g6e0v/Z5UNJ/kTRwsQXM7H5J90vS0NCQkiSRJE1MTKjRaKhUam0g1Ot1VavVzuMhBJXLZZVKJWUyGUnS2NiYstls5001MTGhZrOpvr6+OdtoNpsaGxu7oI1cLqdcrnXxmWq1qhBCp43JyUnVajUNDAyc10Z/f796elrfY5TLZeXz+U4b4+PjMjMVi8VOG5OTk+rv75ckNRoNVSqV89oYHR1VsVhUNpvttNHT06NCoSBJqtVqqtfrF7QxMDAgM5uzjUqlokwmc14bU1NTndd4ampK4+PjnTamX+O+vr7ON4SVSkW9vb3nvcYrsZ+KxSL9tAL6SVqd76fp2ldrP927o6GDx8+pp8d0w1Wt9R47O65jZ1t13LujoUptSk++eFq3X7dRuUyrjY8fGtb1mwY6yzxz7Kzy2Yy2D7bW+8UzFQ2P1rT32vVKkkR7tk7o6ZfO6M7tG9XbruPh507qpqE1nTYOHD2jUj6rl29s9e2Lpyo6M17Tnq2tNnZtqerA0bO6+/pB9ZipGYIeeX5Yu7as1dq+nJIk0UBhWOv68p0J6xdGxlSp1bVryzolSaKbh8Z18Ng53bNjU6vvm009emhEe7au00AhqyRJVMoNazDJ6+p1rTYODZdVqze0c2itJGm4PKHnT5Z11/bB1mveaOrxwyPae816lfK9SpJEhexJDa0tamhtq1+ePTGqZjPops1rJEmFQkHZTI/uuG5jqx/rU3riyGndum29itlWG9nMCW1eW9S97Vpn91OhUFAhm9Ft2za0MjpHP0nSjS9LNDjQyv7sfsrn8yrlerX32vWtbEzUL+gnSbp5aI02lFq5na+fJOns+OQF/SSp009S6xD62f2UyWQ6/9dTldq8/SRJT75w+oJ+6u3tXZT303QdJ0arOjJSuaCf+vv7O8s8dnhE2zaWdFVSPK+fpte7Ese96c+nnp4e5fP5VTfuTb/GK/3zabVvRxSLRfppBfTT9Gu8EvtpPpbWjeTN7A2S7gsh/ICZvUbSj4QQ3jDfc2655Zawb9++VOoBZsrlcpqcnPQuA5Fa7flb6KJn3VwQ60qXWWnrWchi1rplXZ+Onpn7djqxvSbdrmcxLFYeV7rVPv5heSN/SNvu3bufCCHcNtdjaR5qfo+kbzKzI5L+VNJXmdkfpbg+oGuNRsO7BESM/MFTpVb3LgERY/yDJ/IHT6kdah5C+DFJPyZJM/Z4vzmt9QGXolQqaXR01LsMRIr8wdOuLev00HMnvcvAZVrpt9Fj/IMn8gdPS3FVcwAAAAAAorUk19QPIXxU0keXYl1AN+p1DrWEH/IHT6cqNe8SEDHGP3gif/DEHm9EqVqtepeAiJE/eDp47Jx3CYgY4x88kT94YuKNKE3fEgHwQP7gafp2WoAHxj94In/wxMQbAAAAAIAUdTXxNrOrzOw9ZvbB9s87zex70i0NSE9a968HukH+4Gmq2fQuARFj/IMn8gdP3V5c7b2Sfk/ST7R/flbSPknvSaEmIHXlctm7BESM/MHTo4dGvEtYcea7hZe0Mm7jtVww/sET+YOnbg813xhC+DNJTUkKIUxJ4g70WLFKpZJ3CYgY+YOnPVvXeZeAiDH+wRP5g6duJ94VM9sgKUiSmd0picuiYsXKZDLeJSBi5A+eBgpZ7xIQMcY/eCJ/8NTtoeb/WdL7JW03s4clDUr6ttSqAgAAAABglehq4h1C+JSZfaWkGyWZpM+HELgDPVassbEx7xIQMfIHT0++cNq7BESM8Q+eyB88zTvxNrNvuchDN5iZQgh/lUJNQOqy2axqtZp3GYgU+YOnwSSvysiUdxmIFOMfPJE/eFpoj/c3tv/eJOluSf/c/vm1kh6RxMQbK1I+n2fghRvyB09XryvpyEjFuwxEivEPnsgfPM078Q4hvE2SzOzDknaGEI63f96s1i3GAAAAAADAPLq9qvnW6Ul32wlJ16RQD7AkJiYmvEtAxMgfPB0a5j628MP4B0/kD566var5P5nZhyS9r/3zmyT9YzolAelrNpveJSBiKzl/D+w/Pu/jD963eYkqweWq1RveJaxK8703eF982Uoe/7DykT946mqPdwjh7ZJ+S9Ke9p/fDiG8I83CgDT19fV5l4CIkT942jm01rsERIzxD57IHzx1u8d7+grmXEwNAAAAAIBL0NUebzO708w+YWZjZjZpZg0zG027OCAt9Tq3oYcf8gdPw2XOcYQfxj94In/w1O3F1X5N0rdLek5SUdL3Svr1tIoC0latVr1LQMTIHzw9f5KLq8EP4x88kT946nbirRDC85IyIYRGCOH3JL0+vbKAdCVJ4l0CIkb+4Omu7YPeJSBijH/wRP7gqdtzvMfNLCfpKTP7BUnHdQmTdgAAAAAAYtXt5PktkjKS3i6pImmrpG9NqyggbdxOAp7IHzxNNsgf/DD+wRP5g6eu9niHEF5o/7Mq6afSKwdYGmNjY94lIGLkD54ePzziXQIixvgHT+QPnuadeJvZZySFiz0eQnjFolcELIFSqaRKpeJdBiJF/uBp7zXr9eSLp73LQKQY/+CJ/MHTQnu839D++wfbf/9h++83a54JObDcZTIZ7xIQMfIHT6V8t5d3ARYf4x88kT94mvfTd/oQczP7mhDC3hkP/aiZfUrSu9IsDgAAAACAla7bi6uZmd0z44e7L+G5wLLDOT7wRP7g6ZNHTnmXgIgx/sET+YOnbifP3yPpN8zsiJm9IOk3JH13emUB6crlct4lIGLkD56G1ha9S0DEGP/gifzBU7dXNX9C0h4zW9P++VyqVQEpy+VympiY8C4DkVqu+Xtg//F5H3/wvs1LVAnSNLS2T4eH2esDH8t1/EMcyB88LXRV8zeHEP7IzP7zrN9LkkIIv5RibQAAAAAArHgL7fEutf8eSLsQYClVq1XvEhAx8gdPz54Y9S4BzjyPbmH8gyfyB08LXdX8t9p//9TSlAMsjRC4Gx78kD94ajbJH/ww/sET+YOnri6uZma/YGaJmWXN7J/MbNjM3px2cUBa+vr6vEtAxMgfPN20eY13CYgY4x88kT946vaq5l8bQhiV9AZJRyRdL+n/SqsoAAAAAABWi24n3tOHpH+DpD/nquZY6SYnJ71LQMTIHzydGOUcR/hh/IMn8gdPXd1OTNIHzOygpKqk7zezQUlcix8rVq1W8y4BESN/8HRkpOJdAiLG+AdP5A+eutrjHUJ4l6S7Jd0WQqhLqkh6Y5qFAWkaGOBC/fBD/uDpjus2epeAiDH+wRP5g6du93hL0k2StpnZzOf8wSLXAwAAAADAqtLVxNvM/lDSdklPSWq0fx3ExBsrVLPZ9C4BESN/8FStT3mXgIgx/sET+YOnbvd43yZpZ+Dmd1glxsbGvEtAxMgfPD1x5LR3CYgY4x88kT946vaq5gckvSzNQoCl1N/f710CIkb+4OnWbeu9S0DEGP/gifzBU7d7vDdKesbMHpfUuRxgCOGbLvYEMytI+hdJ+fZ6/iKE8JNXUCuwaHp6uv3OCVh85A+eitlLubwLsLgY/+CJ/MFTt5++776MtmuSviqEMGZmWUkPmdkHQwiPXkZbAAAAAACsSF1NvEMIHzOzayXtCCH8o5n1Scos8JwgafpEimz7D+eIY1kol8veJSBi5A+eHjs84l0CIsb4B0/kD566var5/ynpfknr1bq6+RZJvynpdQs8LyPpCUnXS/r1EMJjcyxzf7ttDQ0NKUkSSdLExIQajYZKpZIkqV6vq1qtdh4PIahcLqtUKimTaX0HMDY2pmw2q3w+32mj2Wyqr69vzjaazabGxsYuaCOXyymXy0mSqtWqQgidNiYnJ1Wr1Tr3AZxuo7+/v3P4SrlcVj6f77QxPj4uM1OxWOy0MTk52TnPpNFoqFKpnNfG6OioisWistlsp42enh4VCgVJUq1WU71ev6CNgYEBmdmcbVQqFWUymfPamJqa6rzGU1NTGh8f77Qx/Rr39fWpt7e300Zvb+95r/FK7KdsNqvTp0/TT8u8n6TV+X4qFouq1+uL2k9/fGBcknRouKxavaGdQ2slScPlCT1/sqz///+4YcF+unfHJknSsydG1WwG3bR5jSTpxGhVR0YqSpJE9+5oqFqf0hNHTuvWbes7hy0/dnhE2zaWOsscPH5OPT2mG65q1X7s7LiOna12Hq/UpvTki6d1+3Ublcu0+unjh4Z1/aaBzjLPHDurfDaj7YOtfHzxTEXDozXtvXa9kiTRnq0TevqlM7pz+0b1tvv64edO6qahNZ02Dhw9o1I+q5dvbPXti6cqOjNe056trTZ2banqwNGzuvv6QfWYqRmCHnl+WLu2rNXavpySJNFAYVjr+vK6ZkOrX74wMqZKra5dW9YpSRLdPDSug8fO6Z726zfVbOrRQyPas3WdBgpZJUmiUm5Yg0leV68rzdtPd20fbOW60dTjh0e095r1KuV7lSSJCtmTGlpb1NDavjn7qVAoKJvp6dyne3Y/JUmibOaE/s0Nm1Sbal3Zd3Y/FQoFFbIZ3bZtQyvnc/STJN34skSDA63sz+6nfD6vUq5Xe69tnUtenqhf0E+SdPPQGm0otbI/Xz9J0tnxyQv6SVKnnyTp6ZdOX9BPmUymk+tTldq8/SRJT75w+oJ+6u3t7bRxsX4qlUqdZT555NQF/TSzjen30+x+6u/v7ywz/X66Kime10/TuZ5+P83up27HvXt3NM57P83up+kxJ43Pp6mpKTUaDT6flunn02rfjshmszp37hz9tMz7afo1Xon9NB/r5kLlZvaUpNslPRZC2Nv+3WdCCLsXfHJr2bWS/lrSO0IIBy623C233BL27dvXTZPAFUmSRKOjo95lIFJp5O+B/cfnffzB+zYvShtXusxitLEa17OQxaz13h2b9NBzJ1Nfz5W00Y2VtJ6lzGM3FmO8uFx8/sIT+UPadu/e/UQI4ba5Huv2CgO1EMLk9A9m1qtLOGw8hHBW0kckvb7b5wAAAAAAsBp0O/H+mJn9uKSimX2NpD+X9LfzPcHMBtt7umVmRUlfI+ngFdQKLJrx8XHvEhAx8gdPB4+f8y4BEWP8gyfyB0/dTrzfJWlY0mck/UdJ+yX91wWes1nSR8zs05I+IekfQggfuNxCgcW00DkYQJrIHzz19JA/+GH8gyfyB0/dXtW8aWZ/I+lvQgjDXT7n05L2XkFtQGqmL24FeCB/8HTDVYlOjk54l4FIMf7BE/mDp3kn3tb6WugnJb1d7b3jZtaQ9KshhP+efnkAsPp5XugIAAAA6VvoUPN3SrpH0leEENaHENZLukPSPWb2ztSrA1IyOTm58EJASsgfPB07yzmO8MP4B0/kD54Wmni/RdK3hxC+MP2LEMJhSW+W9NY0CwPSxMALT+QPno6drXqXgIgx/sET+YOnhSbe2RDCyOxfts/zzqZTEpC+/v5+7xIQMfIHT7dt2+BdAiLG+AdP5A+eFpp4z/e1EF8ZAQAAAACwgIWuar7HzEbn+L1JKqRQD7AkGo2GdwmIGPmDp0ptyrsEpGi5X6yR8Q+eyB88zTvxDiFklqoQYClVKhXvEhAx8gdPT7542rsERIzxD57IHzx1dR9vYLXp7+/X2NiYdxmI1OXkb769WN57sLCy3H7dRj1++ILLtwBLgs9feCJ/8LTQOd7AqtTTQ/Thh/zBUy5D/uCH8Q+eyB88sccbAAAAHcv9PHEAWIn42gdRGh2d65qBwNIgf/D08UPD3iUgYox/8ET+4ImJN6JULBa9S0DEyB88Xb9pwLsERIzxD57IHzxxqDmilM1mVa1WvctApLzyt9Dho4jD4EBBn/8Se33gg89feCJ/8MQebwAAAAAAUsTEG1EaHx/3LgERI3/w9Myxs94lIGKMf/BE/uCJiTeixO0k4In8wVM+m/EuARFj/IMn8gdPpA9RKhQK3iUgYuQPnrYPcnE1+GH8gyfyB09MvAEAAAAASBETb0SpVqt5l4CIkT94+uKZincJiBjjHzyRP3hi4o0o1et17xIQMfIHT8OjbHjCD+MfPJE/eGLijSj19/d7l4CIkT942nvteu8SEDHGP3gif/DExBsAAAAAgBQx8UaUGo2GdwmIGPmDp/IEh1rCD+MfPJE/eGLijShVKlxcCH7IHzw9/dIZ7xIQMcY/eCJ/8MTEG1EaGOA+tvBD/uDpzu0bvUtAxBj/4In8wRMTb0TJzLxLQMTIHzz19vDRDz+Mf/BE/uCJT18AAAAAAFLExBtRGh0d9S4BESN/8PTwcye9S0DEGP/gifzBExNvRKlYLHqXgIiRP3i6aWiNdwmIGOMfPJE/eGLijShls1nvEhAx8gdPG0p57xIQMcY/eCJ/8MTEGwAAAACAFDHxRpS4jyM8kT94OnCU+3jDD+MfPJE/eGLijShlMhnvEhAx8gdPpTyHWsIP4x88kT94YuKNKBUKBe8SEDHyB08v39jvXQIixvgHT+QPnnq9CwAAAMDK8sD+4/M+/uB9m5eoEgBYGdjjjSjVajXvEhAx8gdPL57iHEf4YfyDJ/IHT0y8EaWpqSnvEhAx8gdPZ8bZ8IQfxj94In/wxMQbUSqVSt4lIGLkD572bF3vXQIixvgHT+QPnph4AwAAAACQIibeiBKHGsET+YOns+OT3iUgYox/8ET+4Cm1ibeZbTWzj5jZM2b2WTP7obTWBVyq8fFx7xIQMfIHTweOnvUuARFj/IMn8gdPae7xnpL0wyGEnZLulPSDZrYzxfUBXRsYGPAuAREjf/B09/WD3iUgYox/8ET+4Cm1iXcI4XgI4VPtf5clfU7SlrTWB1wKM/MuAREjf/DUQ/7giPEPnsgfPPUuxUrMbJukvZIem+Ox+yXdL0lDQ0NKkkSSNDExoUaj0bn6YL1eV7Va7TweQlC5XFapVFImk5EkjY2NKZvNKp/Pd9poNpvq6+ubs41ms6mxsbEL2sjlcsrlcpKkarWqEEKnjcnJSdVqtc43ZtNt9Pf3q6en9T1GuVxWPp/vtDE+Pi4zU7FY7LQxOTmp/v5+SVKj0VClUjmvjdHRURWLRWWz2U4bPT09KhQKklr3IazX6xe0MTAw0BlUZrdRqVSUyWTOa2NqaqrzGk9NTWl8fLzTxvRr3NfXp97e3k4bvb29573GK7GfCoUC/bQC+klane+n6edM99O9OzZJkr4wMqZKra5dW9ZJkk5Vajp47JySJNG9Oxqaajb16KER7dm6TgOFVh1PvnBa+Xy+08ah4bJq9YZ2Dq2VJA2XJ/T8yXKnjclGU48fHtHea9arlG/l5ZNHTmlobVFDa1v98uyJUTWbQTdtXiNJOjFa1ZGRSqeNan1KTxw5rVu3rVcx22rjscMj2rax1Fnm4PFz6ukx3XBVKx/Hzo7r2Nlq5/FKbUpPvnhat1+3UblMq58+fmhY128a6CzzzLGzymcz2j7YyscXz1Q0PFrT3mvXK0kS7dk6oadfOqM7t29Ub7uvH37upG4aWtNp48DRMyrls3r5xlbfvniqojPjNe3Z2mpj15aqDhw9q7uvH1SPmZoh6JHnh7Vry1qt7cspSRINFIa1ri+vazaULuinJEl089C4Dh47p3vafTC7n5IkUSk3rMEkr6vXlebtp7u2t/ZGz+6nJElUyJ6ct58KhYKymR7dcd3G1vttVj8lSaJs5oSuWlPo5GV2PxUKBRWyGd22bUMro3P0kyTd+LJEgwOtHM/up3w+r1KuV3uvbV09vTxRv6CfJOnmoTXaUGqNL/P1k9Q6L312P0nq9JMkPf3S6Qv6KZPJdP6v0++ni/XT9Ptpdj/NfI9erJ9KpVJnmbneTzPbmH4/ze6n/v7+zjLT76erkuJ5/TSd6+n30+x+mtnG9Ptpdj9NtzHz/XSxfpp+P83up+k25uunJEnm/HwyM+XzeT6flunn02rfjigUCvTTCuin6dd4JfbTfCy0P7zSYmb9kj4m6WdCCH8137K33HJL2LdvX6r1AMBy88D+4/M+/uB9m+ddZqHHu11mIYuxnsWqdbWtZyHLqdbV9Jos1Xpife0BIDa7d+9+IoRw21yPpXpVczPLSvpLSX+80KQbWErT38ABHsgfPO3asta7BESM8Q+eyB88pXaoubX2tb9H0udCCL+U1nqAyzF9iA5wpRba+zQX8gdP04dmAx4Y/+CJ/MFTmnu875H0FklfZWZPtf/cl+L6AAAAAABYdlL72ieE8JAkLh2IZalSqXiXgIiRP3h6+qXT3iUgYox/8ET+4CnVc7yB5YpDjeCJ/MHTur68dwmIGOMfPJE/eGLijShN3zIB8ED+4Gn6dluAB8Y/eCJ/8MTEGwAAAACAFDHxRpQmJia8S0DEyB88fWFkzLsERIzxD57IHzwx8UaUGo2GdwmIGPmDp0qt7l0CIsb4B0/kD56YeCNKpRLnOMIP+YOnXVvWeZeAiDH+wRP5gycu7QcAAIBF98D+4xf87t4dDT303Ek9eN/mVNczbTHXAwBXgj3eiFK9zqGW8EP+4OlUpeZdAiJG/uCJz194Yo83olStVr1LQMTIHzwdPHbOuwREbGb+5ttTLbG3GouPz194Yo83opQkiXcJiBj5g6d7dmzyLgERI3/wxOcvPDHxBgAAAAAgRUy8EaUQgncJiBj5g6epZtO7BESM/METn7/wxMQbUSqXy94lIGLkD54ePTTiXQIiRv7gic9feGLijShxH0d4In/wtGcr9/GGH/IHT3z+whMTb0Qpk8l4l4CIkT94GihkvUtAxMgfPPH5C0/cTgwAUjTX7XLu3dHQQ8+dlMTtcgAgbdy2DMBywB5vRGlsbMy7BETsyRdOe5eAiJE/eCJ/8MT2HzyxxxtRymazqtVq3mUgUoNJXpWRKe8yECnyB0+Xmj/2VmMxsf0HT+zxRpTy+bx3CYjY1eu4uAv8kD94In/wxPYfPDHxBgAAAAAgRUy8EaWJiQnvEhCxQ8PcRxR+yB88kT94YvsPnph4I0rNZtO7BESsVm94l4CIkT94In/wxPYfPHFxNUSpr69Po6Oj3mUgUjuH1nZuJwYsNfIHTys1f1zkbXVg+w+e2OMNAAAAAECK2OONKNXrde8SsAKktYdjuMw5ZvBD/uCJ/MET23/wxB5vRKlarXqXgIg9f5KLC8EP+YMn8gdPbP/BExNvRClJEu8SELG7tg96l4CIkT94In/wxPYfPDHxBgAAAAAgRUy8ESVuJwFPkw3yBz/kD57IHzyx/QdPTLwRpbGxMe8SELHHD494l4CIkT94In/wxPYfPDHxRpRKpZJ3CYjY3mvWe5eAiJE/eCJ/8MT2Hzwx8UaUMpmMdwmIWCnPnRzhh/zBE/mDJ7b/4ImJNwAAAAAAKWLijShxjg88ffLIKe8SEDHyB0/kD57Y/oMnJt6IUi6X8y4BERtaW/QuAREjf/BE/uCJ7T944kQbRCmXy2liYsK7DFymB/Yfn/fxB+/bvESVXJ6htX06PMy37vBB/uCJ/MET23/wxB5vAAAAAABSxMQbUapWq94lIGLPnhj1LgERI3/wRP7gie0/eGLijSiFELxLQMSaTfIHP+QPnsgfPLH9B0+pTbzN7HfN7KSZHUhrHcDl6uvr8y4BEbtp8xrvEhAx8gdP5A+e2P6DpzT3eL9X0utTbB8AAAAAgGUvtYl3COFfJJ1Oq33gSkxOTnqXgIidGOUcM/ghf/BE/uCJ7T944hxvRKlWq3mXgIgdGal4l4CIkT94In/wxPYfPLnfx9vM7pd0vyQNDQ0pSRJJ0sTEhBqNhkqlkiSpXq+rWq12Hg8hqFwuq1QqKZPJSJLGxsaUzWaVz+c7bTSbzc75HLPbaDabGhsbu6CNXC6nXC4nqXX1wxBCp43JyUnVajUNDAyc10Z/f796elrfY5TLZeXz+U4b4+PjMjMVi8VOG5OTk+rv75ckNRoNVSqV89oYHR1VsVhUNpvttNHT06NCoSCpNXDU6/UL2hgYGJCZzdlGpVJRJpM5r42pqanOazw1NaXx8fFOG9OvcV9fn3p7eztt9Pb2nvcar8R+KhaLOnnyJP20zPtJmvv9tCkp6IarWus9dnZcx85Wddu2Da3/e21Kkhaln+7cvlG97TYefu6kbhpaow2l1utx4OgZ5XI53btjkyTpxVMVnRmvac/W9ZKks+Otb9Xvvn5QPWZqhqBHnh/Wri1rddf1g/rcsXN6+qXTyufznTa+MDKmSq2uXVvWSZJOVWo6eOyckiTRvTsammo29eihEe3Zuk4Dhdb/5ckXzm/j0HBZtXpDO4fWSpKGyxN6/mS508Zko6nHD49o7zXrVcq38vLJI6c0tLaoobWtfnn2xKiazdA5F/PEaFVHRiqdNqr1KT1x5LRu3bZexWyrjccOj2jbxlJnmYPHz6mnxy7op+nHK7UpPfniad1+3UblMq3X+OOHhnX9poHOMs8cO6t8NqPtg618fPFMRcOjNe29dr2SJNGerRN6+qUzc/bTdBsHjp5RKZ/Vyzf2X9BPSZJo15aqDhw9O2c/re3LKUkSDRSGta4vr2s2lC7opyRJdPPQuA4eO6d72n0wu5+SJFEpN6zBJK+r15Xm7ae7tg+23huz+ilJEhWyJ+ftp0KhoGymR3dct7H1fpvVT0mSKJs5oX/7qq06fra113F2PxUKBRWymfPeT7P7SZJufFmiwYHW+2d2P+XzeZVyvdp7beu9UJ6oX9BPknTzrPfTxfpp+v00u58kdfpJkp5+6fQF/ZTJZDrvjen308X6afr9NLufent7O21crJ9KpVJnmbneTzPbmH4/ze6n/v7+zjLT76erkuJ5/TSd67nGvSdfPL+N6ffT7H6abmPm++li/TTXuFfKZzttzNdPSZLo7uunzns/SVIxm9HnvzTaaeNi4949OzYpSRLdub0+bz8lSaLNa89e9P2UJIluv64+77iXJMmCn0+3bqtddNy7KikqSRK2I1bAdkSxWNSpU6fop2XeT9Ov8Ursp/lYmlf3M7Ntkj4QQtjVzfK33HJL2LdvX2r1ANOSJNHoKLc0Wake2H983scfvG/zgssspJs2FlrmYo/fu2OTHnruZOrrudRlFrKcal1t61nIYtY6M39prudK2ujGSloPefyy6fwtt9dkIYvRBvyx/Ye07d69+4kQwm1zPcah5ohSs9n0LgERq9anvEtAxMgfPJE/eGL7D57SvJ3Y+yR9XNKNZvZFM/uetNYFXKqxsTHvEhCxJ45w3Un4IX/wRP7gie0/eErzqubfHkLYHELIhhCuDiG8J611AZdq+twOwMOt29Z7l4CIkT94In/wxPYfPHGoOaLU00P04Wf6wjyAB/IHT+QPntj+gydGPwAAAOAKcQE2APPhax9EqVwue5eAiD12eMS7BESM/MET+YMntv/giT3eiFI+n9fExIR3GavOUt3GZqXbtrGk507w4Q8f5A+eyB88sf0HT+zxRpRyuZx3CYjYVUnRuwREjPzBE/mDJ7b/4Ik93gAAAIjalR6NBQALYY83ojQ+Pu5dAiJ28Pg57xIQMfIHT+QPntj+gycm3oiSmXmXgIj19JA/+CF/8ET+4IntP3hi4o0oFYucYwY/N1yVeJeAiJE/eCJ/8MT2Hzwx8QYAAAAAIEVcXA1Rmpyc9C4BETt2lnPM4If8wVPs+evmtptID9t/8MQeb0SJgReejp2tepeAiJE/eCJ/8MT2HzyxxxtR6u/v1+joqHcZS4Zv2JeX27Zt0EPPnfQuA5Eif/BE/uAptu0/LC/s8QYAAAAAIEVMvBGlRqPhXQIiVqlNeZeAiJE/eCJ/8MT2Hzwx8UaUKpWKdwmI2JMvnvYuAREjf/BE/uCJ7T94YuKNKPX393uXgIjdft1G7xIQMfIHT+QPntj+gycuroYo9fTwndPlmO8ibVygrXu5DPmDH/IHT+QPntj+gyfSBwAAAABAiph4I0rcSgKePn5o2LsERIz8wRP5gye2/+CJiTeiVCwWvUtAxK7fNOBdAiJG/uCJ/MET23/wxDneiFI2m1W1WvUuA5EaHCjo81/iW3f4IH/wRP6WBtdkmRvbf/DEHm8AAAAAAFLEHm9EaXx83LsEROyZY2e9S0DEyB88kb/5zbenWop7b/ViYPsPntjjjShxOwl4ymcz3iUgYuQPnsgfPLH9B0+kD1EqFAreJSBi2we5uBD8kD94In/wxPYfPHGoOeCom0PKluqwMw5vAwBg+ePzGliZ2OONKNVqNe8SELEvnql4l4CIkT94In/wxPYfPLHHG1Gq1+sLLrPQrTiW0zfO3DZkZRke5YMffsgfPJG/5WE5bcMspW62/4C0sMcbUerv7/cuARHbe+167xIQMfIHT+QPntj+gyf2eAMAAAC4ZCvpiLsH9h/XvTsaeui5kxc8ttxqxerEHm9EqdFoeJeAiJUnONQNfsgfPJE/eCJ/8MTEG1GqVLi4C/w8/dIZ7xIQMfIHT+QPnsgfPHGoOaI0MDCgcrmc+noWungJ4nTn9o169NCIdxmIFPmDJ/KHS7WYF4Ijf/DEHm9Eycy8S0DEensYeuGH/MET+YMn8gdP7PHGqhPrLTIAAACWk262yRbj6EC2/bAS8LUPojQ6OupdAiL28BxXVAWWCvmDJ/IHT+QPnph4I0rFYtG7BETspqE13iUgYuQPnsgfPJE/eGLijShls1nvEhCxDaW8dwmIGPmDJ/IHT+QPnjjHe4Vbbee0rLb/DwAAwErENtmFeE0uxGvSvVT3eJvZ683s82b2vJm9K811AZeC+3jD04Gj3EcUfsgfPJE/eCJ/8JTaxNvMMpJ+XdLXS9op6dvNbGda6wMuRSaT8S4BESvlOdUBfsgfPJE/eCJ/8JTmoea3S3o+hHBYkszsTyW9UdIzKa5zycx3WEWsh1Rc6e0gun3dFuO1/5PPVvXQPFe2jLUPsTRevrFfR8+Me5eBSJE/eCJ/8DRf/hbrkOmFtlOX06HZy2XbfTm9JmlK81DzLZJemvHzF9u/AwAAAAAgGhZCSKdhs2+T9PoQwve2f36LpDtCCG+ftdz9ku5v/3ijpM+nUhBwvo2SRryLQLTIHzyRP3gif/BE/pC2a0MIg3M9kOah5kclbZ3x89Xt350nhPDbkn47xTqAC5jZJ0MIt3nXgTiRP3gif/BE/uCJ/MFTmoeaf0LSDjN7uZnlJP17Se9PcX0AAAAAACw7qe3xDiFMmdnbJX1IUkbS74YQPpvW+gAAAAAAWI7SPNRcIYT9kvanuQ7gMnF6AzyRP3gif/BE/uCJ/MFNahdXAwAAAAAA6Z7jDQAAAABA9Jh4Y9Uys981s5NmduAij68xs781s6fN7LNm9ralrhGrVxf5W2dmf21mnzazx81s11LXiNXLzLaa2UfM7Jn2+PZDcyxjZva/zOz5dg5f5VErVp8u83eTmX3czGpm9iMedWJ16jJ/39Ee9z5jZo+Y2R6PWhEXJt5Yzd4r6fXzPP6Dkp4JIeyR9BpJ/7N9BX5gMbxX8+fvxyU9FUJ4haS3SvqVpSgK0ZiS9MMhhJ2S7pT0g2a2c9YyXy9pR/vP/ZL+v6UtEatYN/k7Lek/SfrFpS4Oq143+fuCpK8MIeyW9NPi3G8sASbeWLVCCP+i1gf7RReRNGBmJqm/vezUUtSG1a+L/O2U9M/tZQ9K2mZmVy1FbVj9QgjHQwifav+7LOlzkrbMWuyNkv4gtDwqaa2ZbV7iUrEKdZO/EMLJEMInJNUdSsQq1mX+HgkhnGn/+Kikq5e2SsSIiTdi9muSbpZ0TNJnJP1QCKHpWxIi8rSkb5EkM7td0rXigx8pMLNtkvZKemzWQ1skvTTj5y/qwsk5cEXmyR+Qui7z9z2SPrgkBSFqTLwRs6+T9JSkIUmvlPRrZpZ4FoSo/JxaexifkvQOSU9KarhWhFXHzPol/aWkB0IIo971IC7kD566yZ+ZvVatifePLmVtiFOq9/EGlrm3Sfq50Lqn3vNm9gVJN0l63LcsxKC9EfA2qXWRK7XONzvsWhRWFTPLqrXR+cchhL+aY5GjkrbO+Pnq9u+AK9ZF/oDUdJM/M3uFpN+R9PUhhFNLWR/ixB5vxOxFSa+TpPa5tTeKiQ+WiJmtnXExv++V9C/sEcJiaX+Z8x5Jnwsh/NJFFnu/pLe2r25+p6RzIYTjS1YkVq0u8wekopv8mdk1kv5K0ltCCM8uZX2Il7V29gGrj5m9T62rlW+UdELST0rKSlII4TfNbEitK09vlmRq7f3+I5disep0kb+7JP2+Whf5+6yk75lxoRfgipjZvZL+Va3rV0xfu+LHJV0jdTJoal3r4vWSxiW9LYTwSYdyscp0mb+XSfqkpKS9zJiknXwBiSvVZf5+R9K3Snqh/fhUCOG2pa4VcWHiDQAAAABAijjUHAAAAACAFDHxBgAAAAAgRUy8AQAAAABIERNvAAAAAABSxMQbAAAAAIAUMfEGAAAAACBFTLwBACuWmf2EmX3WzD5tZk+Z2R1OdXyXmf3aJSz/GjM7167502b2j2a2aYHnvNLM7rvM+l5jZh/oYrn3tet5p5k9YGZ9l7O+dlvvNbNvu4Tlt5nZf7jc9c3R3iNdLHPEzDbO8fvXmNndi1ULAABMvAEAK5KZ3SXpDZJeFUJ4haSvlvSSb1WX5F9DCK9s1/4JST+4wPKvlHRZE+9umNnLJH1FCOEVIYRflvSApMueeF+GbZKueOJtZr2SFEK4konzayQx8QYALBom3gCAlWqzpJEQQk2SQggjIYRjkmRmrzOzJ83sM2b2u2aWb//+iJn9j/ae5k+a2avM7ENmdsjMvq+9TL+Z/ZOZfar9/DfOtXIze5uZPWtmj0u6Z8bvB83sL83sE+0/98z1/BnLm6QBSWfaP5faNT/e/j+80cxykv67pDe1a3+Tmd1uZh9vL/OImd3YzYs2V/vthz4saUu7/Z+UNCTpI2b2kTnauNXMPmZmT7Rfv80XWd1Xt1/nZ83sDe3nZszs/22/Np82s//YXvbnJL26vf53tveA/2u7Hz413x7o9h7qfzWz90t6pv27sfbfPWb2G2Z20Mz+wcz2z9oT/44ZfX2TmW2T9H2S3tmu5dXdvK4AAMyn17sAAAAu04cl/Tcze1bSP0raF0L4mJkVJL1X0utCCM+a2R9I+n5JD7af92II4ZVm9svt5e6RVJB0QNJvSpqQ9M0hhNH2YciPmtn7QwhhesXtieZPSbpV0jlJH5H0ZPvhX5H0yyGEh8zsGkkfknTzHPW/2syekrRBUkXSj7d//xOS/jmE8N1mtlbS4+3/33+TdFsI4e3tGhJJrw4hTJnZV0v6WUnf2sXrdkH7ZvaPkr5J0gdCCK9st/82Sa8NIYzMfLKZZSX9qqQ3hhCGzexNkn5G0nfPsa5tkm6XtF2tSfz1kt4q6VwI4SvaX4g8bGYflvQuST8SQpieoPdJ+poQwoSZ7ZD0Pkm3zfP/epWkXSGEL8z6/be069gpaZOkz0n63RmPj4QQXmVmP9Be//ea2W9KGgsh/OI86wMAoGtMvAEAK1IIYczMbpX0akmvlbTPzN6l1gT4CyGEZ9uL/r5ah3E/2P75/e2/PyOpP4RQllQ2s1p7IlqR9LNm9m8kNSVtkXSVpC/NWP0dkj4aQhiWJDPbJ+mG9mNfLWlna0e2JCkxs/4Qwtis/8K/zphk/qikX1BrT+vXSvomM/uR9nIFSdfM8RKskfT77UlpkJSd7/Wa4WLtV7t8/o2Sdkn6h/b/MSPp+EWW/bMQQlPSc2Z2WNJN7fW/YsZe5zWSdkianPXcrKRfM7NXSmroy6/vxTw+x6Rbku6V9OftOr40xx78v2r//YRak3QAABYdE28AwIoVQmhI+qikj5rZZyR9p7685/liau2/mzP+Pf1zr6TvkDQo6dYQQt3Mjqg1Oe1Wj6Q7QwgTl/Cc90v6y/a/TdK3hhA+P3MBu/DCcT8t6SMhhG9uHx790S7XdbH2t13C8z8bQriri2XDHD+bpHeEED40a/2vmbXsOyWdkLRHrdd0odez0kU9c5nOQENsFwEAUsI53gCAFcnMbmzv7Z32SkkvSPq8pG3tw5ol6S2SPnYJTa+RdLI96X6tpGvnWOYxSV9pZhvah17/uxmPfVjSO2bU+cou1nmvpEPtf39IrfOOrf38ve3fl9U6F3xmnUfb//6uLtYx7WLtzzZ7fdM+L2nQWhe3k5llzeyWi7Tx79rnWG+XdF37uR+S9P3t101mdoOZleZY3xpJx9t7qt+i1p71y/GwpG9t13GVWhdOW8jF/u8AAFwWJt4AgJWqX61DrZ8xs0+rdQ7vu9t7mt8m6c/be8Gbap273a0/lnRb+7lvlXRw9gIhhOOS3i3p42pN7D434+H/1H7+p83sGbUOH5/L9IXEnlZrYvnD7d//tFqHWX/azD7b/llqnUe+s/2cN6l1aPr/MLMndWl7ai/W/my/LenvZx+aHUKYlPRtkn6+XftTuvgVwF9U6xz1D0r6vnbf/I5aF0D7lJkdkPRb7fo/LalhZk+b2Tsl/Yak72yv4yZd/h7tv5T0xfY6/0jSp9Q6L38+fyvpm7m4GgBgsdiMa8UAAACsOtPn2JvZBrW+CLgnhPClhZ4HAMBi4VwmAACw2n2gfeG8nKSfZtINAFhq7PEGAGCVMLOvk/Tzs379hRDCN3vUs9jMbLekP5z161oIYfaF5wAAWFaYeAMAAAAAkCIurgYAAAAAQIqYeAMAAAAAkCIm3gAAAAAApIiJNwAAAAAAKWLiDQAAAABAiv437h3rJNRCmGEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.hist((beta_left + beta_right), density=True, alpha=0.8, bins=100, rwidth=0.9)\n",
    "\n",
    "plt.title('Posteriori')\n",
    "plt.xlabel('Soma de Beta_left e beta_right')\n",
    "plt.ylabel('Densidade')\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.4)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "740fc814",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparação com os beta indivíduais\n",
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.hist(beta_left, density=True, alpha=0.8, bins=100, rwidth=0.9)  # Beta left\n",
    "\n",
    "plt.hist(beta_right, density=True, alpha=0.8, bins=100, rwidth=0.9)  # Beta Right\n",
    "\n",
    "plt.title('Comparativo entre as Posterioris de Beta Left e Beta Right')\n",
    "plt.xlabel('Betas')\n",
    "plt.ylabel('Densidade')\n",
    "\n",
    "plt.grid(ls='--', color='white', alpha=0.1)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ad90f92",
   "metadata": {},
   "source": [
    "### RCode 6.7 - Pag 166"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01dcbd5a",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning in '/tmp/httpstan_jd5k56to/model_5wzmeslf.stan', line 19, column 54: A\n",
      "    normal distribution is given parameter sigma as a scale parameter\n",
      "    (argument 2), but sigma was not constrained to be strictly positive.\n",
      "Warning in '/tmp/httpstan_jd5k56to/model_5wzmeslf.stan', line 17, column 8: Parameter\n",
      "    sigma is given a exponential distribution, which has strictly positive\n",
      "    support, but sigma was not constrained to be strictly positive.\n",
      "Warning in '/tmp/httpstan_jd5k56to/model_5wzmeslf.stan', line 15, column 27: Argument\n",
      "    100 suggests there may be parameters that are not unit scale; consider\n",
      "    rescaling with a multiplier (see manual section 22.12).\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -0.7425, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  Gradient evaluation took 1.9e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -1.61947, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  Gradient evaluation took 7.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.72 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.207287, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -0.643273, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -1.11551, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  Gradient evaluation took 2.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.177542, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -0.558744, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  Gradient evaluation took 2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.776509, but must be nonnegative! (in '/tmp/httpstan_xcgeqomu/model_5wzmeslf.stan', line 17, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] leg_left;\n",
    "        vector[N] height;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real beta_left;\n",
    "        real sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        alpha ~ normal(10, 100);\n",
    "        beta_left ~ normal(2, 10);\n",
    "        sigma ~ exponential(1);\n",
    "        \n",
    "        height ~ normal(alpha + beta_left * leg_left, sigma);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(height),\n",
    "    'leg_left': leg_left,\n",
    "    'height': height,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)\n",
    "\n",
    "alpha = samples['alpha'].flatten()\n",
    "beta_left = samples['beta_left'].flatten()\n",
    "sigma = samples['sigma'].flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8662c085",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.83</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_left</th>\n",
       "      <td>2.02</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.67</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.58</td>\n",
       "      <td>0.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean   std  7.0%  93.0%\n",
       "alpha      0.83  0.32  0.25   1.40\n",
       "beta_left  2.02  0.07  1.90   2.14\n",
       "sigma      0.67  0.05  0.58   0.75"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# RCode 6.7 - Continuação\n",
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b0dd7405",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Leg Left')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5455cb83",
   "metadata": {},
   "source": [
    "### R Code 6.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1dc086a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>kcal.per.g</th>\n",
       "      <th>perc.fat</th>\n",
       "      <th>perc.lactose</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.940041</td>\n",
       "      <td>-1.217243</td>\n",
       "      <td>1.307262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.816126</td>\n",
       "      <td>-1.030355</td>\n",
       "      <td>1.011285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.125913</td>\n",
       "      <td>-1.391531</td>\n",
       "      <td>1.382679</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.001998</td>\n",
       "      <td>-1.335535</td>\n",
       "      <td>1.586874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.258511</td>\n",
       "      <td>-0.469693</td>\n",
       "      <td>0.257115</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   kcal.per.g  perc.fat  perc.lactose\n",
       "0   -0.940041 -1.217243      1.307262\n",
       "1   -0.816126 -1.030355      1.011285\n",
       "2   -1.125913 -1.391531      1.382679\n",
       "3   -1.001998 -1.335535      1.586874\n",
       "4   -0.258511 -0.469693      0.257115"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('data/milk.csv', sep=';')\n",
    "\n",
    "df_std = df[['kcal.per.g', 'perc.fat', 'perc.lactose']].copy()\n",
    "\n",
    "df_std['kcal.per.g'] = (df_std['kcal.per.g'] - df_std['kcal.per.g'].mean()) / df_std['kcal.per.g'].std()\n",
    "df_std['perc.fat'] = (df_std['perc.fat'] - df_std['perc.fat'].mean()) / df_std['perc.fat'].std()\n",
    "df_std['perc.lactose'] = (df_std['perc.lactose'] - df_std['perc.lactose'].mean()) / df_std['perc.lactose'].std()\n",
    "\n",
    "df_std.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c9a0786c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kcal.per.g      0\n",
       "perc.fat        0\n",
       "perc.lactose    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Não tem nenhum 'missing values'\n",
    "\n",
    "df_std.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2a0a1c7",
   "metadata": {},
   "source": [
    "### R Code 6.9 - Pag 167"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "01800c46",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 1.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.13 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "# kcal.per.g  regredido em perc.fat\n",
    "\n",
    "model_kf = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] outcome;\n",
    "        vector[N] predictor;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real beta;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        alpha ~ normal(0, 0.2);\n",
    "        beta ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "        \n",
    "        outcome ~ normal(alpha + beta * predictor, sigma);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data_kf = {\n",
    "    'N': len(df_std['kcal.per.g']),\n",
    "    'outcome': list(df_std['kcal.per.g'].values),\n",
    "    'predictor': list(df_std['perc.fat'].values),\n",
    "}\n",
    "\n",
    "posteriori_kf = stan.build(model_kf, data=data_kf)\n",
    "samples_kf = posteriori_kf.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4f31f6ca",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 1.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.6e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "# kcal.per.g  regredido em  perc.lactose\n",
    "\n",
    "model_kl = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] outcome;\n",
    "        vector[N] predictor;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real beta;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        alpha ~ normal(0, 0.2);\n",
    "        beta ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "        \n",
    "        outcome ~ normal(alpha + beta * predictor, sigma);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data_kl = {\n",
    "    'N': len(df_std['kcal.per.g']),\n",
    "    'outcome': df_std['kcal.per.g'].values,\n",
    "    'predictor': df_std['perc.lactose'].values,\n",
    "}\n",
    "\n",
    "posteriori_kl = stan.build(model_kl, data=data_kl)\n",
    "samples_kl = posteriori_kl.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "cb3ee955",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>0.86</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.68</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.49</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  0.00  0.08 -0.15   0.15\n",
       "beta   0.86  0.09  0.68   1.02\n",
       "sigma  0.49  0.07  0.36   0.61"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples_kf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3682ce19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples_kf, title='perc.fat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "dd83e730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.07</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>-0.90</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-1.04</td>\n",
       "      <td>-0.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.53</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  0.00  0.07 -0.14   0.12\n",
       "beta  -0.90  0.08 -1.04  -0.77\n",
       "sigma  0.41  0.06  0.32   0.53"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples_kl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7eb79bd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples_kl, title='perc.lactose')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c3bd67a",
   "metadata": {},
   "source": [
    "### R Code 6.10  -  pag 167"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c1d9331b",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning in '/tmp/httpstan_s69tliti/model_r3zhhfk6.stan', line 22, column 40: A\n",
      "    normal distribution is given parameter sigma as a scale parameter\n",
      "    (argument 2), but sigma was not constrained to be strictly positive.\n",
      "Warning in '/tmp/httpstan_s69tliti/model_r3zhhfk6.stan', line 20, column 8: Parameter\n",
      "    sigma is given a exponential distribution, which has strictly positive\n",
      "    support, but sigma was not constrained to be strictly positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -0.444329, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: exponential_lpdf: Random variable is -0.0103946, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  Gradient evaluation took 2.6e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.0667496, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.605486, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 5.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -3.09717, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 4.9e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -313.877, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -6.18116, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 3.3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.33 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: exponential_lpdf: Random variable is -0.452598, but must be nonnegative! (in '/tmp/httpstan_u59ke11e/model_r3zhhfk6.stan', line 20, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] F;  // Fat\n",
    "        vector[N] L;  // Lactose\n",
    "        vector[N] K;  // kcal/g\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real bF;\n",
    "        real bL;\n",
    "        real sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        alpha ~ normal(0, 0.2);\n",
    "        bF ~ normal(0, 0.5);\n",
    "        bL ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "        \n",
    "        K ~ normal(alpha + bF*F + bL*L, sigma);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(df_std['kcal.per.g']),\n",
    "    'F': df_std['perc.fat'].values,\n",
    "    'L': df_std['perc.lactose'].values,\n",
    "    'K': df_std['kcal.per.g'].values,\n",
    "}\n",
    "\n",
    "posteriori_FL = stan.build(model, data=data)\n",
    "samples_FL = posteriori_FL.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2638a212",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.07</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bF</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bL</th>\n",
       "      <td>-0.67</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-1.02</td>\n",
       "      <td>-0.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.41</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.52</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  0.00  0.07 -0.13   0.14\n",
       "bF     0.25  0.20 -0.09   0.62\n",
       "bL    -0.67  0.20 -1.02  -0.31\n",
       "sigma  0.41  0.06  0.31   0.52"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples_FL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c1437e49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples_FL, title='Perc.Fat & Perc.Lactose')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f157828",
   "metadata": {},
   "source": [
    "### R Code 6.11 - Pag 168 - Figure 6.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "871153f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.plotting.scatter_matrix(df_std, diagonal='hist', grid=True, figsize=(17, 6))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77836161",
   "metadata": {},
   "source": [
    "### R Code 6.12 - Overthinking - Rever"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1c05e493",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] kcal_per_g;\n",
    "        vector[N] perc_fat;\n",
    "        vector[N] new_predictor_X;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real bF;\n",
    "        real bX;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        kcal_per_g ~ normal(alpha + bF * perc_fat + bX * new_predictor_X, sigma);\n",
    "    }\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "17f90206",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_predictor_x(r=0.9):\n",
    "    N = len(df['perc.fat'].values)\n",
    "    \n",
    "    mean = r * df['perc.fat'].values\n",
    "    sd = np.sqrt((1 - r**2) * np.var(df['perc.fat'].values))\n",
    "    \n",
    "    return np.random.normal(mean, sd, N)  # New Predictor X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "8855ae68",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data_dict(r=0.9):\n",
    "    data = {\n",
    "        'N': len(df['kcal.per.g']),\n",
    "        'kcal_per_g': df['kcal.per.g'].values,\n",
    "        'perc_fat': df['perc.fat'].values,\n",
    "        'new_predictor_X': generate_predictor_x(r=r),\n",
    "    }\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "258dfb4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def adjust_model(r=0.9):\n",
    "    \n",
    "    parameter_mean_samples  = []\n",
    "    \n",
    "    for _ in range(1):  # In book running 100x\n",
    "        # Runnning the model\n",
    "        posteriori = stan.build(model, data=generate_data_dict(r=r))\n",
    "        samples = posteriori.sample(num_chains=4, num_samples=1000)\n",
    "        \n",
    "        # Get parameter slope mean\n",
    "        parameter_mean_samples.append(samples['bF'].flatten().mean())\n",
    "            \n",
    "    return parameter_mean_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "51dd0f33",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 5.4e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.54 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 2.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.28 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 3.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.38 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  80% (6400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 1.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.4e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.14 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  80% (6400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 9e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 5e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 9e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  85% (6800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 9e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 9e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 5e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 8e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning: The parameter sigma has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bX has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter bF has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n",
      "Warning: The parameter alpha has no priors. This means either no prior is\n",
      "    provided, or the prior(s) depend on data variables. In the later case,\n",
      "    this may be a false positive.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   9% (700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  34% (2700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  59% (4700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  84% (6700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_8d2sm6wp/model_72hqbwsd.stan', line 17, column 8 to column 81)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 7e-06 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.07 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "stddev = []\n",
    "r_sequence = np.arange(0, 0.99, 0.1)  # In book using 0.01\n",
    "\n",
    "for r in r_sequence:\n",
    "    parameter = adjust_model(r=r)\n",
    "    stddev.append(np.mean(parameter))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "94bedff6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "plt.plot(r_sequence, stddev)\n",
    "plt.xlabel(\"correlation\", fontsize=14)\n",
    "plt.ylabel(\"stddev\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2a2d01e",
   "metadata": {},
   "source": [
    "### R Code 6.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "08d57d29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>h0</th>\n",
       "      <td>100.0</td>\n",
       "      <td>9.782726</td>\n",
       "      <td>2.138707</td>\n",
       "      <td>4.168524</td>\n",
       "      <td>8.279903</td>\n",
       "      <td>9.642072</td>\n",
       "      <td>11.353860</td>\n",
       "      <td>14.316299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1</th>\n",
       "      <td>100.0</td>\n",
       "      <td>14.209396</td>\n",
       "      <td>2.766929</td>\n",
       "      <td>6.881795</td>\n",
       "      <td>12.512818</td>\n",
       "      <td>14.190085</td>\n",
       "      <td>15.688766</td>\n",
       "      <td>20.786965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>treatment</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.502519</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fungus</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.270000</td>\n",
       "      <td>0.446196</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           count       mean       std       min        25%        50%  \\\n",
       "h0         100.0   9.782726  2.138707  4.168524   8.279903   9.642072   \n",
       "h1         100.0  14.209396  2.766929  6.881795  12.512818  14.190085   \n",
       "treatment  100.0   0.500000  0.502519  0.000000   0.000000   0.500000   \n",
       "fungus     100.0   0.270000  0.446196  0.000000   0.000000   0.000000   \n",
       "\n",
       "                 75%        max  \n",
       "h0         11.353860  14.316299  \n",
       "h1         15.688766  20.786965  \n",
       "treatment   1.000000   1.000000  \n",
       "fungus      1.000000   1.000000  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(3)\n",
    "\n",
    "# Quantidade de plantas\n",
    "N = 100\n",
    "\n",
    "# Simulação inicial das alturas\n",
    "h0 = np.random.normal(10, 2, N)\n",
    "\n",
    "# Atribuindo tratamentos e simulando fungos e tratamentos\n",
    "treatment = np.repeat([0,1], repeats=int(N/2))\n",
    "fungus = np.random.binomial(n=1, p=(0.5 - treatment*0.4), size=N)\n",
    "h1 = h0 + np.random.normal(5 - 3*fungus, 1, N)\n",
    "\n",
    "# Dataframe\n",
    "d = pd.DataFrame.from_dict({'h0': h0, \n",
    "                            'h1': h1, \n",
    "                            'treatment': treatment, \n",
    "                            'fungus': fungus})\n",
    "d.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b6fd9a7",
   "metadata": {},
   "source": [
    "### R Code 6.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e288a443",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sim_p</th>\n",
       "      <td>10000.0</td>\n",
       "      <td>1.02366</td>\n",
       "      <td>0.259148</td>\n",
       "      <td>0.391611</td>\n",
       "      <td>0.83898</td>\n",
       "      <td>0.993265</td>\n",
       "      <td>1.174575</td>\n",
       "      <td>2.781105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count     mean       std       min      25%       50%       75%  \\\n",
       "sim_p  10000.0  1.02366  0.259148  0.391611  0.83898  0.993265  1.174575   \n",
       "\n",
       "            max  \n",
       "sim_p  2.781105  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_p = np.random.lognormal(0, 0.25, int(1e4))\n",
    "pd.DataFrame(sim_p, columns=['sim_p']).describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1069b797",
   "metadata": {},
   "source": [
    "### R Code 6.15"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "489bb597",
   "metadata": {},
   "source": [
    "Modelo:\n",
    "\n",
    "$$ h_{1,i} \\sim Normal(\\mu_i, \\sigma) $$\n",
    "\n",
    "$$ \\mu_i = h_{0, i} \\times p $$\n",
    "\n",
    "Prioris: \n",
    "\n",
    "$$ p \\sim LogNormal(0, 0.25) $$\n",
    "\n",
    "$$ sigma \\sim Exponential(1) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "13a32efc",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 2.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 1.6e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 2.7e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.27 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_tmv3g7y8/model_jd4qfihi.stan', line 18, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N; \n",
    "        vector[N] h1;\n",
    "        vector[N] h0;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real<lower=0> p;\n",
    "        real<lower=0> sigma;\n",
    "        \n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        mu = h0 * p;\n",
    "        \n",
    "        h1 ~ normal(mu, sigma);\n",
    "        \n",
    "        // Prioris\n",
    "        p ~ lognormal(0, 0.25);\n",
    "        sigma ~ exponential(1); \n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'h1': h1,\n",
    "    'h0': h0,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4204aa47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>1.43</td>\n",
       "      <td>0.02</td>\n",
       "      <td>1.39</td>\n",
       "      <td>1.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.98</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.73</td>\n",
       "      <td>2.23</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "p      1.43  0.02  1.39   1.46\n",
       "sigma  1.98  0.14  1.73   2.23"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89468587",
   "metadata": {},
   "source": [
    "### RCode 6.16"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59ea7655",
   "metadata": {},
   "source": [
    "Modelo *post-treatment bias*:\n",
    "\n",
    "$$ h_{1, i} \\sim Normal(\\mu_i, \\sigma) $$\n",
    "\n",
    "$$ \\mu_i = h_{0, i} \\times p $$\n",
    "\n",
    "$$ p = \\alpha + \\beta_T T_i + \\beta_F F_i $$\n",
    "\n",
    "prioris:\n",
    "\n",
    "$$ \\alpha \\sim LogNormal(0, 0.25) $$\n",
    "\n",
    "$$ \\beta_T \\sim Normal(0, 0.5) $$\n",
    "\n",
    "$$ \\beta_F \\sim Normal(0, 0.5) $$\n",
    "\n",
    "$$ \\sigma \\sim Exponential(1) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d1446add",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning in '/tmp/httpstan_3v2pqc1w/model_2uvo3jva.stan', line 28, column 8: Parameter\n",
      "    alpha is given a lognormal distribution, which has strictly positive\n",
      "    support, but alpha was not constrained to be strictly positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 3.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 5.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.777686, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.73154, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -0.884237, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Gradient evaluation took 4.7e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.47 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -440.313, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -440.044, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -109.303, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -26.7802, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -5.91942, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.729029, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -1.22763, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.22602, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.0862, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Gradient evaluation took 4.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.45 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -2620.37, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -75.8589, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.380928, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "To mu definition below\n",
    "----------------------\n",
    "\n",
    "vector[N] a;\n",
    "vector[N] b;\n",
    "vector[N] c; \n",
    "\n",
    "These operation:\n",
    "c = a .* b;\n",
    "\n",
    "Is the same operation:\n",
    "for (n in 1:N) {\n",
    "  c[n] = a[n] * b[n];\n",
    "}\n",
    "\n",
    "Reference:\n",
    "https://mc-stan.org/docs/reference-manual/arithmetic-expressions.html\n",
    "\"\"\"\n",
    "\n",
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] h0;\n",
    "        vector[N] h1;\n",
    "        vector[N] T;  // Treatment\n",
    "        vector[N] F;  // Fungus\n",
    "    }\n",
    "\n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real bT;\n",
    "        real bF;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "\n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        vector[N] p;\n",
    "        \n",
    "        p = alpha + bT * T + bF * F;\n",
    "        mu = h0 .* p;  \n",
    "    \n",
    "        // likelihood\n",
    "        h1 ~ normal(mu, sigma);\n",
    "    \n",
    "        // prioris\n",
    "        alpha ~ lognormal(0, 0.25);\n",
    "        bT ~ normal(0, 0.5);\n",
    "        bF ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'h0': h0,\n",
    "    'h1': h1,\n",
    "    'T': treatment,\n",
    "    'F': fungus,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "219ff496",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.53</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.48</td>\n",
       "      <td>1.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bT</th>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bF</th>\n",
       "      <td>-0.32</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.39</td>\n",
       "      <td>-0.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.44</td>\n",
       "      <td>0.11</td>\n",
       "      <td>1.26</td>\n",
       "      <td>1.64</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  1.53  0.03  1.48   1.59\n",
       "bT    -0.03  0.04 -0.09   0.03\n",
       "bF    -0.32  0.04 -0.39  -0.25\n",
       "sigma  1.44  0.11  1.26   1.64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "82e65448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Treatment and Fungus')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc4cabcc",
   "metadata": {},
   "source": [
    "### R Code 6.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "9f0f2fc7",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.5 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 4.7e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.47 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 2.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 3.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] h0;\n",
    "        vector[N] h1;\n",
    "        vector[N] T;  // Treatment\n",
    "    }\n",
    "\n",
    "    parameters {\n",
    "        real<lower=0> alpha;\n",
    "        real bT;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        vector[N] p;\n",
    "\n",
    "        p = alpha + bT * T;\n",
    "        mu = h0 .* p;\n",
    "\n",
    "        h1 ~ normal(mu, sigma);\n",
    "\n",
    "        alpha ~ lognormal(0, 0.2);\n",
    "        bT ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'h0': h0,\n",
    "    'h1': h1,\n",
    "    'T': treatment,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "8ba3cbb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.36</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.31</td>\n",
       "      <td>1.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bT</th>\n",
       "      <td>0.13</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.89</td>\n",
       "      <td>0.14</td>\n",
       "      <td>1.65</td>\n",
       "      <td>2.14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  1.36  0.03  1.31   1.41\n",
       "bT     0.13  0.04  0.06   0.20\n",
       "sigma  1.89  0.14  1.65   2.14"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2427af81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Treatment without fungus')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f248c83",
   "metadata": {},
   "source": [
    "### R Code 6.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "0a3add94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.DiGraph()\n",
    "\n",
    "nodes = {0: '$H_0$', \n",
    "         1: '$H_1$', \n",
    "         2: 'F', \n",
    "         3: 'T'}\n",
    "\n",
    "for i in nodes:\n",
    "    G.add_node(nodes[i])\n",
    "\n",
    "edges = [(nodes[0], nodes[1]),\n",
    "         (nodes[2], nodes[1]),\n",
    "         (nodes[3], nodes[2])]\n",
    "\n",
    "G.add_edges_from(edges)\n",
    "\n",
    "# explicitly set positions\n",
    "pos = {nodes[0]: (0, 0), \n",
    "       nodes[1]: (1, 0), \n",
    "       nodes[2]: (1.5, 0), \n",
    "       nodes[3]: (2, 0)}\n",
    "\n",
    "options = {\n",
    "    \"font_size\": 15,\n",
    "    \"node_size\": 400,\n",
    "    \"node_color\": \"white\",\n",
    "    \"edgecolors\": \"white\",\n",
    "    \"linewidths\": 1,\n",
    "    \"width\": 1,\n",
    "}\n",
    "\n",
    "nx.draw(G, pos, with_labels=True, **options)\n",
    "\n",
    "# Set margins for the axes so that nodes aren't clipped\n",
    "ax = plt.gca()\n",
    "# ax.margins(0.01)\n",
    "plt.axis(\"off\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d3574ba",
   "metadata": {},
   "source": [
    "### R Code 6.19"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15741a2d",
   "metadata": {},
   "source": [
    "$$F \\_||\\_ H_0$$\n",
    "\n",
    "$$H_0 \\_||\\_ T$$\n",
    "\n",
    "$$ H_1 \\_||\\_ T | F $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "493beb12",
   "metadata": {},
   "source": [
    "### R Code 6.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "58dc30c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>h0</th>\n",
       "      <td>100.0</td>\n",
       "      <td>10.091610</td>\n",
       "      <td>1.976358</td>\n",
       "      <td>6.313914</td>\n",
       "      <td>8.850678</td>\n",
       "      <td>10.169278</td>\n",
       "      <td>11.369749</td>\n",
       "      <td>15.273222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>h1</th>\n",
       "      <td>100.0</td>\n",
       "      <td>16.510702</td>\n",
       "      <td>2.715874</td>\n",
       "      <td>10.105379</td>\n",
       "      <td>14.711143</td>\n",
       "      <td>15.899131</td>\n",
       "      <td>18.671828</td>\n",
       "      <td>22.662508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>treatment</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.502519</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>fungus</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.480000</td>\n",
       "      <td>0.502117</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           count       mean       std        min        25%        50%  \\\n",
       "h0         100.0  10.091610  1.976358   6.313914   8.850678  10.169278   \n",
       "h1         100.0  16.510702  2.715874  10.105379  14.711143  15.899131   \n",
       "treatment  100.0   0.500000  0.502519   0.000000   0.000000   0.500000   \n",
       "fungus     100.0   0.480000  0.502117   0.000000   0.000000   0.000000   \n",
       "\n",
       "                 75%        max  \n",
       "h0         11.369749  15.273222  \n",
       "h1         18.671828  22.662508  \n",
       "treatment   1.000000   1.000000  \n",
       "fungus      1.000000   1.000000  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.random.seed(3)\n",
    "\n",
    "# Quantidade de plantas\n",
    "N = 100\n",
    "\n",
    "# Simulação inicial das alturas\n",
    "h0 = np.random.normal(10, 2, N)\n",
    "\n",
    "# Atribuindo tratamentos e simulando fungos e tratamentos\n",
    "treatment = np.repeat([0, 1], repeats=int(N/2))\n",
    "\n",
    "M = np.random.binomial(n=1, p=0.5, size=N)  # Moisture -> Bernoulli(p=0.5)\n",
    "\n",
    "fungus = np.random.binomial(n=1, p=(0.5 - treatment * 0.4 + 0.4 * M), size=N)\n",
    "h1 = h0 + np.random.normal((5 + 3 * M), 1, N)\n",
    "\n",
    "# Dataframe\n",
    "d2 = pd.DataFrame.from_dict({'h0': h0, \n",
    "                            'h1': h1, \n",
    "                            'treatment': treatment, \n",
    "                            'fungus': fungus})\n",
    "d2.describe().T "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "50038aa0",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 2.6e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 2.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 2.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.22 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 3.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Location parameter[1] is inf, but must be finite! (in '/tmp/httpstan_zszojnzt/model_iiartt5i.stan', line 22, column 8 to column 31)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "# RCode 6.17 with new database\n",
    "\n",
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] h0;\n",
    "        vector[N] h1;\n",
    "        vector[N] T;  // Treatment\n",
    "    }\n",
    "\n",
    "    parameters {\n",
    "        real<lower=0> alpha;\n",
    "        real bT;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        vector[N] p;\n",
    "\n",
    "        p = alpha + bT * T;\n",
    "        mu = h0 .* p;\n",
    "\n",
    "        h1 ~ normal(mu, sigma);\n",
    "\n",
    "        alpha ~ lognormal(0, 0.2);\n",
    "        bT ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'h0': d2.h0.values,\n",
    "    'h1': d2.h1.values,\n",
    "    'T': d2.treatment.values,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "da26d068",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.60</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.55</td>\n",
       "      <td>1.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bT</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>2.16</td>\n",
       "      <td>0.15</td>\n",
       "      <td>1.87</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  1.60  0.03  1.55   1.65\n",
       "bT     0.02  0.04 -0.05   0.09\n",
       "sigma  2.16  0.15  1.87   2.43"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "332e7134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title=\"Only Treatment using d2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5df00a61",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mMessages from \u001b[0m\u001b[36;1mstanc\u001b[0m\u001b[36m:\u001b[0m\n",
      "Warning in '/tmp/httpstan_3v2pqc1w/model_2uvo3jva.stan', line 28, column 8: Parameter\n",
      "    alpha is given a lognormal distribution, which has strictly positive\n",
      "    support, but alpha was not constrained to be strictly positive.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.3 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -2.00689, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.429399, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 4.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.48 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.582579, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -2.80035, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -1.22325, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.73154, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -0.884237, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Gradient evaluation took 5.5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.55 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -314.269, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -314, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -77.7921, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -18.9024, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -3.94998, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.236668, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.22602, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Rejecting initial value:\n",
      "    Error evaluating the log probability at the initial value.\n",
      "  Exception: lognormal_lpdf: Random variable is -1.0862, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  Gradient evaluation took 7.3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.73 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -2854.35, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -83.0723, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.401537, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.176896, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: lognormal_lpdf: Random variable is -0.310218, but must be nonnegative! (in '/tmp/httpstan__bvsoudy/model_2uvo3jva.stan', line 28, column 8 to column 35)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "# RCode 6.16 with new database\n",
    "\n",
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] h0;\n",
    "        vector[N] h1;\n",
    "        vector[N] T;  // Treatment\n",
    "        vector[N] F;  // Fungus\n",
    "    }\n",
    "\n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real bT;\n",
    "        real bF;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "\n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        vector[N] p;\n",
    "        \n",
    "        p = alpha + bT * T + bF * F;\n",
    "        mu = h0 .* p;  \n",
    "    \n",
    "        // likelihood\n",
    "        h1 ~ normal(mu, sigma);\n",
    "    \n",
    "        // prioris\n",
    "        alpha ~ lognormal(0, 0.25);\n",
    "        bT ~ normal(0, 0.5);\n",
    "        bF ~ normal(0, 0.5);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': N,\n",
    "    'h0': d2.h0.values,\n",
    "    'h1': d2.h1.values,\n",
    "    'T': d2.treatment.values,\n",
    "    'F': d2.fungus.values,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "6f42a787",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.53</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.46</td>\n",
       "      <td>1.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bT</th>\n",
       "      <td>0.06</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bF</th>\n",
       "      <td>0.11</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>2.10</td>\n",
       "      <td>0.15</td>\n",
       "      <td>1.83</td>\n",
       "      <td>2.36</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  1.53  0.04  1.46   1.60\n",
       "bT     0.06  0.04 -0.02   0.14\n",
       "bF     0.11  0.04  0.03   0.19\n",
       "sigma  2.10  0.15  1.83   2.36"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1d7c4a70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title=\"Treatments and Fungus\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0da7aad1",
   "metadata": {},
   "source": [
    "## Collider Bias"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c503aea",
   "metadata": {},
   "source": [
    "### 6.21"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab8df1f6",
   "metadata": {},
   "source": [
    "**Simulação**\n",
    "\n",
    "1. Cada ano, $20$ pessoas nascem com valores de felicidade uniformente distribuídos\n",
    "\n",
    "\n",
    "2. Cada ano, cada uma das pessoas envelhece $1$ ano. A sua felicidade não muda.\n",
    "\n",
    "\n",
    "3. Aos $18$ anos, um indivíduo de casa com a probabilidade de porporcional a sua felicidade.\n",
    "\n",
    "\n",
    "4. Uma vez casado, o indivíduo se mantém casado.\n",
    "\n",
    "\n",
    "5. Aos 65 anos, o indivíduo deixa a amostra (Vai morar na Espanha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "dcee492d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function based in https://github.com/rmcelreath/rethinking/blob/master/R/sim_happiness.R\n",
    "# Inv_logit R-function in https://stat.ethz.ch/R-manual/R-devel/library/boot/html/inv.logit.html\n",
    "\n",
    "def inv_logit(x):\n",
    "    return np.exp(x) / (1 + np.exp(x))\n",
    "\n",
    "def sim_happiness(seed=1977 , N_years=1000 , max_age=65 , N_births=20 , aom=18):\n",
    "    np.random.seed(seed)\n",
    "    \n",
    "    df = pd.DataFrame(columns=['age', 'married', 'happiness'])\n",
    "\n",
    "    for i in range(N_years):\n",
    "        # Update age\n",
    "        df['age'] += 1\n",
    "\n",
    "        # Move to Spain when age == max_age\n",
    "        df.drop(df[df['age'] == max_age].index, inplace=True)\n",
    "        \n",
    "        # Will marry?\n",
    "        index_unmarried_aom = df.query((f'age>={aom} and married==0')).index.tolist()\n",
    "        weddings = np.random.binomial(1, inv_logit(df.loc[index_unmarried_aom, 'happiness'] - 4))\n",
    "        df.loc[index_unmarried_aom, 'married'] = weddings\n",
    "        \n",
    "        # New borns\n",
    "        df_aux = pd.DataFrame(columns=['age', 'married', 'happiness'])\n",
    "\n",
    "        df_aux.loc[:, 'age'] = np.zeros(N_births).astype(int)\n",
    "        df_aux.loc[:, 'married'] = np.zeros(N_births).astype(int)\n",
    "        df_aux.loc[:, 'happiness'] = np.linspace(-2, 2, N_births)  # np.random.uniform(0, 1, N_births)\n",
    "        \n",
    "        df = df.append(df_aux, ignore_index=True)\n",
    "        \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3e82c937",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>unique</th>\n",
       "      <th>top</th>\n",
       "      <th>freq</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>5.5%</th>\n",
       "      <th>50%</th>\n",
       "      <th>94.5%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>1300.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>married</th>\n",
       "      <td>1300.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>950.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>happiness</th>\n",
       "      <td>1300.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-8.335213e-17</td>\n",
       "      <td>1.214421</td>\n",
       "      <td>-2.0</td>\n",
       "      <td>-1.789474</td>\n",
       "      <td>-1.110223e-16</td>\n",
       "      <td>1.789474</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            count  unique   top   freq          mean       std  min      5.5%  \\\n",
       "age        1300.0    65.0  64.0   20.0           NaN       NaN  NaN       NaN   \n",
       "married    1300.0     2.0   0.0  950.0           NaN       NaN  NaN       NaN   \n",
       "happiness  1300.0     NaN   NaN    NaN -8.335213e-17  1.214421 -2.0 -1.789474   \n",
       "\n",
       "                    50%     94.5%  max  \n",
       "age                 NaN       NaN  NaN  \n",
       "married             NaN       NaN  NaN  \n",
       "happiness -1.110223e-16  1.789474  2.0  "
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = sim_happiness(seed=1997, N_years=1000)\n",
    "df.describe(percentiles=[0.055, 0.945], include='all').T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "13f82a62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure 6.21\n",
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "colors = ['white' if is_married == 0 else 'blue' for is_married in df.married ]\n",
    "\n",
    "plt.scatter(df.age, df.happiness, color=colors)\n",
    "\n",
    "plt.title('White - Unmarried   |    Blue - Married')\n",
    "plt.xlabel('Age')\n",
    "plt.ylabel('Happiness')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d2aa94d",
   "metadata": {},
   "source": [
    "### R Code 6.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "b071c256",
   "metadata": {},
   "outputs": [],
   "source": [
    "df2 = df[df.age > 17].copy()  # Only adults\n",
    "df2.loc[:, 'age'] = (df2.age - 18) / (65 - 18)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8857a7e0",
   "metadata": {},
   "source": [
    "### R Code 6.23"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b2b5c71",
   "metadata": {},
   "source": [
    "Modelo:\n",
    "\n",
    "$$ happiness \\sim Normal(\\mu_i, \\sigma) $$\n",
    "\n",
    "$$ \\mu_i = \\alpha_{_{MID}[i]} + \\beta_A \\times A_i $$\n",
    "\n",
    "prioris:\n",
    "\n",
    "$$ \\alpha_{_{MID}[i]} \\sim Normal(0, 1)$$\n",
    "\n",
    "$$ \\beta_A \\sim Normal(0, 2) $$\n",
    "\n",
    "$$ \\sigma \\sim Exponential(1); $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "70e19b4f",
   "metadata": {
    "scrolled": true,
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   2% (200/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  10% (800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  15% (1200/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  40% (3200/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  62% (5000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  80% (6400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 0.000115 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.15 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_fshdmqak/model_n7n6r2wh.stan', line 22, column 8 to column 38)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_fshdmqak/model_n7n6r2wh.stan', line 22, column 8 to column 38)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 0.000172 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.72 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 0.000173 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.73 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 0.000164 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.64 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_fshdmqak/model_n7n6r2wh.stan', line 22, column 8 to column 38)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_fshdmqak/model_n7n6r2wh.stan', line 22, column 8 to column 38)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] age;\n",
    "        vector[N] happiness;\n",
    "        array[N] int married;  // Must be integer because this is index to alpha. \n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        vector[2] alpha;  // can also be written like this: real alpha[2] or array[2] int alpha;\n",
    "        real beta_age;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        \n",
    "        for (i in 1:N){\n",
    "            mu[i] = alpha[ married[i] ] + beta_age * age[i];\n",
    "        }\n",
    "        \n",
    "        happiness ~ normal(mu, sigma);\n",
    "        \n",
    "        // Prioris\n",
    "        alpha ~ normal(0, 1);\n",
    "        beta_age ~normal(0, 2);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(df2.happiness.values),\n",
    "    'age': df2.age.values,\n",
    "    'happiness': df2.happiness.values,\n",
    "    'married': df2.married.values + 1  # Because the index in stan starting with 1 \n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "9fdb4842",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha[0]</th>\n",
       "      <td>-0.19</td>\n",
       "      <td>0.06</td>\n",
       "      <td>-0.30</td>\n",
       "      <td>-0.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha[1]</th>\n",
       "      <td>1.38</td>\n",
       "      <td>0.09</td>\n",
       "      <td>1.22</td>\n",
       "      <td>1.53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_age</th>\n",
       "      <td>-0.81</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-1.02</td>\n",
       "      <td>-0.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>0.97</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.93</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean   std  7.0%  93.0%\n",
       "alpha[0] -0.19  0.06 -0.30  -0.07\n",
       "alpha[1]  1.38  0.09  1.22   1.53\n",
       "beta_age -0.81  0.11 -1.02  -0.62\n",
       "sigma     0.97  0.02  0.93   1.02"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "e5aab3a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Married and Unmarried')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8af454d",
   "metadata": {},
   "source": [
    "### R Code 6.24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "c3ed78c6",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   6% (500/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  16% (1300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  22% (1800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  48% (3800/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  66% (5300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  81% (6500/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 0.00011 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.1 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 0.000102 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.02 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 0.000176 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.76 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:\n",
      "  Exception: normal_lpdf: Scale parameter is 0, but must be positive! (in '/tmp/httpstan_6fm3z8ym/model_cddx5h2j.stan', line 21, column 8 to column 38)\n",
      "  If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,\n",
      "  but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.\n",
      "  Gradient evaluation took 0.000138 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 1.38 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] age;\n",
    "        vector[N] happiness;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real beta_age;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        \n",
    "        for (i in 1:N){\n",
    "            mu[i] = alpha + beta_age * age[i];\n",
    "        }\n",
    "        \n",
    "        happiness ~ normal(mu, sigma);\n",
    "        \n",
    "        alpha ~ normal(0, 1);\n",
    "        beta_age ~ normal(0, 2);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(df2.happiness.values),\n",
    "    'happiness': df2.happiness.values,\n",
    "    'age': df2.age.values,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "1791ca51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>-0.00</td>\n",
       "      <td>0.08</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta_age</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.14</td>\n",
       "      <td>-0.23</td>\n",
       "      <td>0.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.22</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.17</td>\n",
       "      <td>1.27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          mean   std  7.0%  93.0%\n",
       "alpha    -0.00  0.08 -0.15   0.14\n",
       "beta_age  0.00  0.14 -0.23   0.27\n",
       "sigma     1.22  0.03  1.17   1.27"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "18979936",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples, title='Without married variable')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2f3083a",
   "metadata": {},
   "source": [
    "### RCode 6.25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2b950c2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 200  # Qty of triads  (G, P, C)\n",
    "\n",
    "b_GP = 1  # Direct effect of G on P \n",
    "b_GC = 0  # Direct effect of G on C\n",
    "b_PC = 1  # Direct effect of P on C\n",
    "b_U  = 2  # Direct effect of U on  P and C"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "156c209f",
   "metadata": {},
   "source": [
    "### R Code 6.26"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "bc860db2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C</th>\n",
       "      <th>P</th>\n",
       "      <th>G</th>\n",
       "      <th>U</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.986995</td>\n",
       "      <td>1.197787</td>\n",
       "      <td>-0.795915</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.715446</td>\n",
       "      <td>3.573636</td>\n",
       "      <td>0.072746</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-4.387763</td>\n",
       "      <td>-3.131400</td>\n",
       "      <td>-0.261240</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.598454</td>\n",
       "      <td>0.462321</td>\n",
       "      <td>-1.298047</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.614388</td>\n",
       "      <td>4.931193</td>\n",
       "      <td>2.676112</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          C         P         G  U\n",
       "0  0.986995  1.197787 -0.795915  1\n",
       "1  5.715446  3.573636  0.072746  1\n",
       "2 -4.387763 -3.131400 -0.261240 -1\n",
       "3  2.598454  0.462321 -1.298047  1\n",
       "4  6.614388  4.931193  2.676112  1"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(3)\n",
    "\n",
    "U = 2 * np.random.binomial(n=1, p=0.5, size=N) - 1  # {-1, 1}\n",
    "# U = np.random.normal(0, 1, N)  # Simulation more realistic example \n",
    "\n",
    "G = np.random.normal(0, 1, size=N)  # Has not influence\n",
    "\n",
    "P = np.random.normal(b_GP*G + b_U*U, 1, size=N)\n",
    "\n",
    "C = np.random.normal(b_PC*P + b_GC*G + b_U*U, 1, size=N)\n",
    "\n",
    "d = pd.DataFrame.from_dict({'C':C, 'P':P, 'G':G, 'U':U})\n",
    "\n",
    "d.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0f4cf8f",
   "metadata": {},
   "source": [
    "### R Code 6.27"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "96fc9f31",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  25% (2000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  50% (4000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  75% (6000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 5.2e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 4.9e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 5e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.5 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 6.9e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.69 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "# C ~ P + G\n",
    "\n",
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] C;\n",
    "        vector[N] P;\n",
    "        vector[N] G;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real b_PC;\n",
    "        real b_GC;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        \n",
    "        for (i in 1:N){\n",
    "            mu[i] = alpha + b_PC*P[i] + b_GC*G[i];\n",
    "        }\n",
    "        \n",
    "        C ~ normal(mu, sigma);\n",
    "        \n",
    "        alpha ~ normal(0, 1);\n",
    "        b_PC ~ normal(0, 1);\n",
    "        b_GC ~ normal(0, 1);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(d.C.values),\n",
    "    'C': d.C.values,\n",
    "    'P': d.P.values,\n",
    "    'G': d.G.values,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "8fe98b4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.07</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_PC</th>\n",
       "      <td>1.77</td>\n",
       "      <td>0.04</td>\n",
       "      <td>1.70</td>\n",
       "      <td>1.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_GC</th>\n",
       "      <td>-0.82</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-1.01</td>\n",
       "      <td>-0.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.33</td>\n",
       "      <td>0.07</td>\n",
       "      <td>1.20</td>\n",
       "      <td>1.45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  0.07  0.10 -0.10   0.24\n",
       "b_PC   1.77  0.04  1.70   1.84\n",
       "b_GC  -0.82  0.10 -1.01  -0.65\n",
       "sigma  1.33  0.07  1.20   1.45"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "4434c499",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "ca6ce4ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1224x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure 6.5\n",
    "plt.figure(figsize=(17, 6))\n",
    "\n",
    "colors = ['black' if u <= 0 else 'blue' for u in U]  # Unobserved\n",
    "\n",
    "x = np.linspace(-3, 4)\n",
    "y = np.mean(samples['alpha']) + np.mean(samples['b_GC']) * x\n",
    "\n",
    "plt.plot(x, y, c='k')\n",
    "\n",
    "plt.scatter(G, C, c=colors)\n",
    "plt.xlabel('Granparent Education (G)')\n",
    "plt.ylabel('GranChild Education (C)')\n",
    "plt.title('Educations - Bias Collider')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93fe0f3b",
   "metadata": {},
   "source": [
    "### R Code 6.28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "03ebe5f8",
   "metadata": {
    "tags": [
     "remove_output"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mBuilding:\u001b[0m found in cache, done.\n",
      "\u001b[36mSampling:\u001b[0m   0%\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   4% (300/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m   8% (600/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  12% (1000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  38% (3000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  59% (4700/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m  80% (6400/8000)\n",
      "\u001b[1A\u001b[0J\u001b[36mSampling:\u001b[0m 100% (8000/8000)\n",
      "\u001b[1A\u001b[0J\u001b[32mSampling:\u001b[0m 100% (8000/8000), done.\n",
      "\u001b[36mMessages received during sampling:\u001b[0m\n",
      "  Gradient evaluation took 9.1e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.91 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 8.8e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.88 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 8.9e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.89 seconds.\n",
      "  Adjust your expectations accordingly!\n",
      "  Gradient evaluation took 7.3e-05 seconds\n",
      "  1000 transitions using 10 leapfrog steps per transition would take 0.73 seconds.\n",
      "  Adjust your expectations accordingly!\n"
     ]
    }
   ],
   "source": [
    "model = \"\"\"\n",
    "    data {\n",
    "        int N;\n",
    "        vector[N] C;\n",
    "        vector[N] P;\n",
    "        vector[N] G;\n",
    "        vector[N] U;\n",
    "    }\n",
    "    \n",
    "    parameters {\n",
    "        real alpha;\n",
    "        real b_PC;\n",
    "        real b_GC;\n",
    "        real b_U;\n",
    "        real<lower=0> sigma;\n",
    "    }\n",
    "    \n",
    "    model {\n",
    "        vector[N] mu;\n",
    "        \n",
    "        for (i in 1:N){\n",
    "            mu[i] = alpha + b_PC*P[i] + b_GC*G[i] + b_U*U[i];\n",
    "        }\n",
    "        \n",
    "        C ~ normal(mu, sigma);\n",
    "        \n",
    "        alpha ~ normal(0, 1);\n",
    "        b_GC ~ normal(0, 1);\n",
    "        b_PC ~ normal(0, 1);\n",
    "        b_U  ~ normal(0, 1);\n",
    "        sigma ~ exponential(1);\n",
    "    }\n",
    "\"\"\"\n",
    "\n",
    "data = {\n",
    "    'N': len(d.C.values),\n",
    "    'C': d.C.values,\n",
    "    'P': d.P.values,\n",
    "    'G': d.G.values,\n",
    "    'U': d.U.values,\n",
    "}\n",
    "\n",
    "posteriori = stan.build(model, data=data)\n",
    "samples = posteriori.sample(num_chains=4, num_samples=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "3296e29e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>7.0%</th>\n",
       "      <th>93.0%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.07</td>\n",
       "      <td>0.07</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_PC</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.86</td>\n",
       "      <td>1.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_GC</th>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.10</td>\n",
       "      <td>-0.22</td>\n",
       "      <td>0.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b_U</th>\n",
       "      <td>1.97</td>\n",
       "      <td>0.17</td>\n",
       "      <td>1.68</td>\n",
       "      <td>2.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sigma</th>\n",
       "      <td>1.02</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.93</td>\n",
       "      <td>1.11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   std  7.0%  93.0%\n",
       "alpha  0.07  0.07 -0.06   0.21\n",
       "b_PC   1.00  0.07  0.86   1.12\n",
       "b_GC  -0.03  0.10 -0.22   0.15\n",
       "b_U    1.97  0.17  1.68   2.27\n",
       "sigma  1.02  0.05  0.93   1.11"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vide.summary(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "8960382f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Vide.plot_forest(samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e5a3524",
   "metadata": {},
   "source": [
    "### R Code 6.29\n",
    "\n",
    "Reference: [*ksachdeva*](https://colab.research.google.com/github/ksachdeva/rethinking-tensorflow-probability/blob/master/notebooks/06_the_haunted_dag_and_the_causal_terror.ipynb#scrollTo=wyUj47f7-kLy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "97881f4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARgAAADgCAYAAADYOHlMAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAZ60lEQVR4nO3debQdVZ328e+TGQIBwmgIMmhDABlMmFTCpDK0CsEFjXmbCIhEBN8WumU58IJo0zR2t7QNNEFoQaRFwLaxRQIqqMgoISQYAiYQwAFUEKUTIGQgv/ePXZckl3tzq+qcOvecU89nrbOSe1O1f5Ws1HN37araWxGBmVkVhgz2AZhZ93LAmFllHDBmVhkHjJlVxgFjZpVxwJhZZRwwZlYZB4yZVcYBY2aVccCYWWUcMGZWmWGDfQDWviQNB/YH9gImAeOBEcAy4ElgNvAA8EBErBqs47T2Jb/saL1JGgdMB04BngHuI4XJU8ByYBSwIyl0JgPDgRnA1RHx4iAcsrUpB4y9TtIQ4DTgPOAGYEZEPDLAPgLeAZwOHAJ8IiK+U/GhWodwwBgAkjYHbgRGAidFxIISbbwTuJrU2zk5IpY29yit03iQ15C0FfAz4H5gcplwAYiIe4E9sy9nSlq/OUdonco9mJqTNBq4F/jviPhCk9ocQurJbAZ8wAPA9eWAqTlJFwNjgWnRxP8MkoaRekXXRcSlzWrXOosDpsYkHQB8C9gtIv5UQfs7AfcA+0bEoma3b+3PAVNjku4GLo2I6yuscQ6wQ0ScVFUNa18OmJqStAfwfWD7iFhZYZ3NgYXAW6roJVl7812k+joFuLJIuEiaIikkTci7T0Q8Twqy40sco3U4B0x9TQZuLbjPVODu7Ncibs3qWc34EqmGJK0HvACMjYhXc+6zAbAAOBi4OSJ2KlBvJ+C2iNi+zPFa53IPpp52AhblDZfMUaSQWAi8IGlSgX0fB7bMQspqxAFTTxsAiwvuMxXoudt0PQUuk7IH7V4CRhesaR3O0zXUUwDKu7GksaQXGXeTFMBQICSdVeDhvCGAn+itGfdg6ukFYIsC2x8DXBsR20bEdhGxDWnqhlwDt5JGknovRXtN1uEcMPX0OLCVpI1ybj8VuKnX975D/suk3YDHI2JZzu2tS/gSqYYi4jVJD5MmjPpxju0P7uN7FxcoOYk0hYPVjHsw9fUD4NgW1ToW+GGLalkb8XMwNZVNi/kYsE1EVDY2kj31excw3pdI9eMeTA1JOpM01+4Y4BMVlzubNC/Mq5KmVFzL2owDpkYknZndZr4ImAPsCpwpaeeK6h1OutO0I7AEuCl7l2lKFfWs/ThgaqCPYNkwIiZGxKPAOcA3stcHmllzC+AK4KMR8XhEjAG2xkFTKx6D6WLZpdBF2ZdzgAMi4qVe2wwBrgU2Ao4p+PpAf3XHArcD34+Ic/v483HAL4ENs28dHRHfbbSutR/3YLrQOnosL/XeNnuM/0TgFdJE3eMarD2BNFXm7cDn+9omIp51j6YeHDBdpEiwrCkiVrB6Koa5kqZl6x0VqT1M0lmkO0aXAJ8e6DUCB0338yVSF8hzKVSgrYnA10gPYc4A/nNdt7GzsZaTgVNJM9dNj4inStb2pVOXccB0sGYGS692BRxEWuXxL0mvFswmrUe9grWXjt2atGDbjIhoytO6Dpru4YDpQFUFSz+1RgG7k8JkPDACWEYKmweBx7JLrCpqO2g6nAOmg7QyWNqJg6ZzOWA6QF2DpTcHTedxwLQxB0vfHDSdwwHThhws+Tho2p8Dpo04WMpx0LQvB0wbcLA0h4Om/ThgBpGDpRoOmvbhgBkEDpbWcNAMPgdMCzlYBoeDZvA4YFrAwdIeHDSt54CpkIOlPTloWscBUwEHS2dw0FTPAdNEDpbO5KCpjgOmCRws3cFB03wOmAY4WLqTg6Z5HDAlOFjqwUHTOAdMAQ6WenLQlOeAycHBYuCgKcMBsw4OFuuLgyY/B0wfHCyWh4NmYA6YNThYrAwHTf8cMDhYrDkcNG9U64BxsFgVHDSr1TJgHCzWCg6amgWMg8UGQ52DphYB42CxdlDHoGlJwEhaj/SPKmBJRLxSeVEcLNaeBjNoJG0IjAZeAxZHxLJK61URMJLWB44D3k1a03h7YAkQpH/UZ0jrGv8UuC4iFje5voPF2l4rgkbSlsA0YH/Subgp6VwcSgqaBcBsYCbwvWavMz6kmY1J2kzSl4FfAx8Efgx8CNgwIjaPiC2ADYAjgVtIAfQrSTMkbd2E+mdKClK4zMnqTnS4WDuKiGcjYgywNemkv0lSSJrSaNuSdpH0LVKATQCuAw4CRkfElhGxGbAJMJ0UMGcAT0s6J+sgNEdENOUDHA08C1wKbFdgv3HAhcBzwAlkvaqCtc8k9Y4CeAjYoFl/L3/8adUnOxcWr/F/eUqJNoYBnwGeBz4FbFxg392BG4CFwLua8ndqwj/KkCxUHgf2b6CdPYGHs6QdsY7tdgX+PqvrYPGn6z59BQ0wBvhHYNw69tsYuBO4vcgP+T7a+WDWWfi7Rv8uDY3BSBoCXAm8FfhANDiWImkUKUEDOCYiVvb686nAfwCjWH155zEW60p9jNGsBF4i9Wzu7LXtGOAO4D7gjIhY1WDt8cCPgGsj4oKy7TQ6BvM5YGfgLxsNF4CIeBU4FhgBfLnn+5JGSLqcFC7rs/q4NwqPsViXitVjNBOybw0j9VJulfRpSQLIfr0emAV8stFwyWr/ljRGerKk48q2U7oHI2kPUldsz4h4puwB9NP2JsA84HjS9eBMYCdSz+VVVif5DhGxtJm1zdqNpDcD80k9+1HAcGAp8BNgKvBXwMeB/aLJd4Ek7Q18H9g9Iv5QeP8yAZNdGj0IXBIRVxduIF+NDwAzSHedNgKWk0a7vwP8AJgfjVzfmXUQSUNJt5mPII2R7Eq61fwMqVd/YETMq6j2BcBfRMSxhfctGTCHke78TKzyJJc0izQa/mXgnuwSyqz2sjGXg4DPA49GxLQKa61HevTkHRHxRJF9y47BnAb8ewt6EOeTbrPd4XAxWy0b87yN1Y95VFlrKXA1cGrRfQsHTDY+cjDwrZzbbyfpkV7fO0/Sp3LsfguwnaS3FD1Osxo4BHgyIubn3UHSVpKul7RI0mxJMyXtmGPXK4FpPQPLeZXpwUwC5kbEyyX2LSS7TX0fsHfVtcw60D7AXXk3zsLhJuCnEfGWiJgEfBbYMsfuT5AGmbcpcoBlA2Z2if3Kmg3s1cJ6Zp2i6Ll4MLAiIi7v+UZEPBwRA4ZUNhwyO6uZW5mA2YF067hVFmY1zWxtRc/Ft9FY52AhUGi4okzAjCQ9i5JXfwPBeQeIX81qmtnaep4La5WlFDwXywTMctKTtnm9QHprc01jgT/m3H94VtPM1lb0XJxPwUucXkZQ8FwsEzC/Jc3vkkv2GP/vJB0CIGkscDhwd84mdshqmtnafkOBc5E0fcpISdN7viFpd0mTc+6/Q1YztzIBU3igB/gwcI6kuaS/5BciYlHOfSeRnho2s7UVOhezgdqjgfdkt6nnk97Q/n3OJgrf4Cn8JK+krYBHgS2b/d5DH7UELAKOjIhHBtrerE4kHQ18PCIObUGtcaTzfmyRlykL92Ai4vfAL0hzVFTtQNLAUu4Hicxq5IfAJEnbtqDWScC3i76pXfZVgctIrwtU7WzSOxBm9kbLSO/q/U2VRbIXLT9Gevm4kLIB813SI/xHlNx/QJL2BfYlDQivknR+0ceUzbqRpGGSbgRWkKYxOVlSoSdsCzodWBQRDxXdsVTARMRy4KPAFZI2LtPGumQz2309qzGKND3D2ThorMZ6BcuxwCWkc/hfgCurOC8kvRU4l9SDKb5/g1NmXgZsBfxV7+ktG2hTwBWkZ2eO7XljW9JI4H+Aw7JN/wE4x3PCWLeTNIw0V3XPfCyXkGau6zk3hpPe2ft2RHypiXU3JN31vS4i/rVUGw0GzEjgZtJ14ImN3lXKJrL6CrAf8O6IWNJPTQeNdb2BgqXXtuNJLz5+JSL+rQm1x5DO7YXA9LLnV0Nz8kZaFW4KaZ7QH0kq8tDPWiS9iRQcE4FD+wqXnpoRcTi+dLIu1d+lUET8TX8nejaH7kHA6ZK+mvU+ytafCNxDui19aiM/vBteeC3SMrA9C6k9IOmTRRZukjRS0kdJS5bMJfVcXsxR10FjXaVMsKwpIn5FmtpkKDBP0pTsDlDe+ptK+gfSRFZfAk6LiNfK/F3WPKhmrueyM/A90vtHXwEOIK2u2Hu79YF3kp4i/ANp8vBJDdYemf3D9Kwlcz4lFnHzx59Wf0irBdy4xv/dixv9v0u6+zoLeJo058sk+lhvjLSU7GGkGeteBK4B3tSsv1tVa1NvB5xCWvZgN9LExMtJPSYB25K6X3cCV0TEgibW9hiNdYQiYywN1NibdDf2XaR3iZ4g/TBeSppMf1PS2mIzgasi4vlm1YYGB3lzFUgj3DuSBqA2IS1PuSDSre4q6zporC21Ilj6qTuadC4+RAqUM4EnognrKPVbs1Xnm6TngM0joqXjIw4aaxeDFSx9HEcA10TEiVXXaniQt92FB4NtkDU6eNvJuj5gejhorNXqHCw9ahMwPRw0VjUHy2q1C5geDhprNgfLG9U2YHo4aKxRDpb+1T5gejhorCgHy8AcML04aGwgDpb8HDD9cNBYbw6W4hwwA3DQmIOlPAdMTg6a+nGwNM4BU5CDpvs5WJrHAVOSg6b7OFiazwHTIAdN53OwVMcB0yQOms7jYKmeA6bJHDTtz8HSOg6Yijho2o+DpfUcMBVz0Aw+B8vgccC0iIOm9Rwsg88B02IOmuo5WNqHA2aQOGiaz8HSfhwwg8xB0zgHS/tywLQJB01xDpb254BpMw6agTlYOocDpk05aN7IwdJ5HDBtzkHjYOlkXb+yY7fRIKxUKWlTYCKwDTACeBV4EpgTEUsqrNsWKyF2G3llR+tPq3o0kraXdKGkJ4GngP8HHEAKmkOAfwJ+L2m+pM9K2qKJtd1j6RIOmA5VVdBIGifpv4BZpN7KUcDGEXFgRJwYEdMj4sMRsR+wMXAy8FZgoaQZksY0UNvB0mUcMB2umUEjaRowF5gPvDki/jYi5kXEqn5qr4iI+yPiZGAHYCgwT9J7C9Z1sHSriGjJB3gulWtNvbp+gJHAbUBkn/OBzwE/B8b3s4+AC4HHgLc3WP9Q4Blg+jq2eRvwCPB/gBvXONaLycYF/an0/0gAX29FrWGVJ5i1VEQsAw5fYzD47OyPXgMekXR0RPyk127nk4Jh/4h4ocH6P5R0IHCHpJURcdWafy7peOCrwPrAN7Nve/C2S/kSqUvF6kunfyKFy1BgI+AWSZ/ruXySNAX4EHBYo+GyRu0ngPcCX5K0Z1ZnhKQrWB0ukH6STgtfCnUtB0z3+yEwB1gOLCaN1fw9cKuk7YDLgBMi4vlmFo2IhcBZwNclbU8aNP4I6RJuMbAM+BlpzMe6lC+RulxE3AHsLWk06Tbz+4EPkJ6jmUN6HuLuispfA0wlDRqvBywgXbbNBO6LiOUV1bU24QftakrSzsADwFsj4g8V1tmHFCq7RcQfq6pj+flBO2uFQ4Gb84aLpNckzZX0sKSHJL0zZ51ZpLtK+5Q9UOtcDpj6OpLVd3HyWBoRe0bEHsBngX/Ms1M2ePufWT2rGQdMDWV3kCaRehdljAH+XGD7WVk9qxkP8tbTDsCSiHiuwD7rSZpLugv1JtL7SHnNBXaVNDwiVhTYzzqcezD1tAVpXKSInkukCcDhwDfyvooQES+T3sAu/Z6SdSYHTD0NA1aW3Tki7gM2AzYvsNsKYHjZmtaZHDD19AowuuzOkiaQngzO9eRv1tMZndW1GvEYTD09DuwoaVhE5O3J9IzBQHo58oSIeC3nvtsCiyNiccHjtA7ngKmhiFgs6bfALsAvcu4ztIGSk4DZDexvHcqXSPV1H/DuFtV6d1bPasYBU19XAR+reuJwSRuS3tb+RpV1rD05YOrrLtKdnUKzz5XwYeAnEfHbiutYG3LA1FT2CP8XgIslrVdFDUlbAZ8HLqiifWt/Dpgai4j/Ig3yfrHZbWeXXpcDV0aEB3hryneR7HRgtqR5EdHMcZLzgDcDxzWxTeswDpiai4jnJR1GmkN3eER8rZH2sp7LF4FjgIOyOYKtpnyJZETEY8DBwGckfTNbybGwbArO24H3AAdUOZGVdQYHjAEQEQuAPUjLy8yTdKakTfLsK2lrSV8EHiTNATy52XP8WmfyJZK9LiJeAc6UdB3wSeBcSTOB+0lP4j5JurU9CtiR9ITu5OzzLeCd2WTfZoADxvoQEbOA47P1po8iBckJwHjScrLLSGHzIPBt4PiIWDJIh2ttzAFj/compLoy+5gV5jEYM6uMA8bMKuOAMbPKOGDMrDIOGDOrjAPGzCrjgDGzyjhgzKwyDhgzq4wDxswq44Axs8o4YMysMg4YM6uMA8bMKuOAMbPKOGDMrDIOGDOrjAPGzCrjgDGzyrQkYCTNADbPfn9jK2qa2dokjZD0s+zLEyR9uuqarerBTFzj95NaVNPM1rYS2GeNr/+i6oKtCpifAauy3/+8RTXNbA0RsQpYkH35MnBv1TVbFTA/B14CXiGFjZkNjruyX1eR1rWqVKsCZjZpDaaV2e/NbHDcR+q9jAIerbpYqwLmaSCA0cC8FtU0szeaTToPF0XEyqqLtWRlx4gISY8Cm0bEq62oaWZ9Wkha+veeVhRTRFTTsDSaNGI9CdgT2IvULbuX1It5EHggIv63kgMwMwCyNcb3JZ2LuwAHAb8BHgbmkHo1D0bE8qbXbnbASHob8HFgKvAYKUjmAC9km2xMCpxJwB7ATcBlEVH5gJNZXUgScAhwOnAw8AApSOYBS0jDI1uRzsO9gPHA14CvRsSvmnUcTbtEkjQG+GfgSOCrwG4R8Uw/m1+b7bM5cDLw35LuAf5vRPyxWcdkVkeStieFxZbAJcAJEbFkgH12InUMZku6FLigGT2apgzySnoXKRmHABMi4rx1hMvrIuL5iLgQmAA8C8yTdHgzjsmsjiR9BJgFzAR2j4jLBwoXgIhYEBFnkK4q9gIeyEKnseNp9BJJ0qHAN4GTIuL7DbY1Gfg28MmIuKGhAzOrGUmfAT4KvD8iftlAOwKmA+cBh0XEL0q31UjASNoPuBmYEhFNGZWWtBvwI+DEiLitGW2adTtJHwf+FjggIn7XpDaPAy4C9o+Ip0q1UTZgsrtEvwA+FRE3lWqk/7YnAzeQungekzFbB0m7kJ6Q3zciFjW57bOA9wGHZK8aFNu/gYC5GNgkIqaVamDg9i8C3hQRU6to36wbSBpGeqbl6xExo4L2h5JeL7guIi4tvH+ZgMlGqWcBO0bEnwo3kK/G+sAvgQ/6FrZZ3yRNBT4BTC7Tw8hZYwIpxN4cES8X2bfsXaSPAddUFS4AEfEKMIN068zM+nYacFFV4QKQDRjfC3yo6L6FA0bScOAjwOU5t99G0lOSxmZfb5J9vV2O3f8D+KCkjYoep1m3k7QrsAPwvZzbS9Ldko5Y43vHSspzM+Uy4NSix1imB7Mr8MeIeDzPxhHxG1JP5MLsWxcCV0TE0zn2fZ40kLx3ieM063YHArdGxIo8G0caDzkVuEjSKEkbABeQnvYdyO3ALpI2LHKAZQJmEsWnXPhXYD9JZwD7A/9SYN/ZpAd/zGxthc/FiHiE9GjJp4FzgW/kufOUhdgjpNd8civzqsBuwNwiO0TEiux2123AoXkTNzMX8NO9VkuSHgA2JA2y3ksKlEezc2h30jBCUV8AHgKWU+yH99ys5l0DbPe6MgEzBnixxH5HAL8D3kZ6kC6vPwNHSqrmtW+zzjCBNMi6ClhP0hPAZqTzo5CIeFnSDcBLEbGswK5/Jp3/uZUJmMInuqQ9gfcC+wF3S7q+wNOGIk21+UrRumZdYPPs19dIM0KOIk0/+wfSzAQq2e4qVs+TnZcoeP6XCZj/BTbNu3H2XsMM4IyI+LWkfyaNwfx1ziY2BX5Q1QN9Zu1M0i2kGejuJJtyISJ+n/3Z/RQ4F5tgU9LslLmVCZiHKTYmcgrw64jouSy6DDhJ0oERcWeO/d9OwTEfs24REe9bxx8/TDo/7m7R4bydNA1EboWf5M0mlLopIipfUyWrdw9wdkT8tBX1zDqFpOnAuyLihBbUGkkag9ksewg2lzK3qR8D1s/eeq6UpPHAzqTXEsxsbT8GjpA0qgW13ke6PCs0Flo4YCLiNeAKWvMI/ymkl6wKvf9gVgcR8QRp+OCYFpQ7jTSWWkjZlx3HkR662bVZc0/0UWMj0suO74mI+VXUMOt0ko4CPg/sU9UyJJImkmbI27bgbe1yLztGxLPAvwOXZ3eJqvBl4H8cLmbrdDNpbOTvqmhc0gjgauCsouECjc0HM5K0YsBFEXF1qUb6b/v9wKWkicMHnE/UrM6yF4cfJE0KVXp6y37avoD09P6RUSIsSq8qEBHLsrko7pD0XETcUratNWUTiF8NHOVwMRtYRDwt6RPATEkHZWMzDZN0OnAc6U5VqZ5IQ6sKZC9OHQlcJemkRi+XJB0NfBf464i4t5G2zOokIq4nTdJ9p6R3NNKWpKGSzgU+Bby358G+Um01Y+G17NmY64CngFOLDvxmc8X8G/AO4PiIuL/hgzKrIUlHku7yXgucGxFLC+4/gXQFsRSYlmf5oXVpyrpIWU9mL9LcLfMlXZbnORlJO2Zz7y4E/gTs4XAxKy8ivkcaM9kWeFzSudld335lE1HtL+k60lvb15Lu3jYULlDN0rHjSGuzTCel4GxWLx0bwCasXjp2LHAVabnKp5t6IGY1l/2Q71nG+VekgeB5pJclh5BWfpxEmtDtZdJrPNdExItNO4ZmB8zrDafZyCeweg3qjUhvYy4h9XTWnNfCzCoiaT3SPC6TgF1IL0+uJP3Qn0M6FxeVHchdZ+2qAsbMrCljMGZmfXHAmFllHDBmVhkHjJlVxgFjZpVxwJhZZRwwZlYZB4yZVcYBY2aVccCYWWUcMGZWmf8PwAculuhC2s8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 266.457x209.764 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dag_6_1 = CausalGraphicalModel(\n",
    "    nodes=[\"C\", \"U\", \"B\", \"A\", \"X\", \"Y\"],\n",
    "    edges=[\n",
    "        (\"U\", \"X\"),\n",
    "        (\"A\", \"U\"),\n",
    "        (\"A\", \"C\"),\n",
    "        (\"C\", \"Y\"),\n",
    "        (\"U\", \"B\"),\n",
    "        (\"C\", \"B\"),\n",
    "        (\"X\", \"Y\"),\n",
    "    ],\n",
    ")\n",
    "\n",
    "pgm = daft.PGM()\n",
    "coordinates = {\n",
    "    \"U\": (0, 2),\n",
    "    \"C\": (4, 2),\n",
    "    \"A\": (2, 3),\n",
    "    \"B\": (2, 1),\n",
    "    \"X\": (0, 0),\n",
    "    \"Y\": (4, 0),\n",
    "}\n",
    "for node in dag_6_1.dag.nodes:\n",
    "    pgm.add_node(node, node, *coordinates[node])\n",
    "for edge in dag_6_1.dag.edges:\n",
    "    pgm.add_edge(*edge)\n",
    "pgm.render()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "6e030064",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "frozenset({'C'})\n",
      "frozenset({'A'})\n"
     ]
    }
   ],
   "source": [
    "all_adjustment_sets = dag_6_1.get_all_backdoor_adjustment_sets(\"X\", \"Y\")\n",
    "\n",
    "for s in all_adjustment_sets:\n",
    "    if all(not t.issubset(s) for t in all_adjustment_sets if t != s):\n",
    "        if s != {\"U\"}:\n",
    "            print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68b50209",
   "metadata": {},
   "source": [
    "### R Code 6.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "49cc5991",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 153.071x153.071 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dag_6_2 = CausalGraphicalModel(\n",
    "    nodes=['S', 'A', 'M', 'W', 'D'],\n",
    "    edges=[\n",
    "        ('S','W'),\n",
    "        ('S','M'),\n",
    "        ('S','A'),\n",
    "        ('A','M'),\n",
    "        ('A','D'),\n",
    "        ('M','D'),\n",
    "        ('W','D'),\n",
    "    ],\n",
    ")\n",
    "\n",
    "# Drawing the DAG\n",
    "pgm = daft.PGM()\n",
    "coordinates = {\n",
    "    \"S\": (0, 2),\n",
    "    \"A\": (0, 0),\n",
    "    \"M\": (1, 1),\n",
    "    \"W\": (2, 2),\n",
    "    \"D\": (2, 0),\n",
    "}\n",
    "for node in dag_6_2.dag.nodes:\n",
    "    pgm.add_node(node, node, *coordinates[node])\n",
    "for edge in dag_6_2.dag.edges:\n",
    "    pgm.add_edge(*edge)\n",
    "pgm.render()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "dfed1764",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "frozenset({'A', 'M'})\n",
      "frozenset({'S'})\n"
     ]
    }
   ],
   "source": [
    "# R Code 6.30\n",
    "\n",
    "all_adjustment_sets = dag_6_2.get_all_backdoor_adjustment_sets(\"W\", \"D\")\n",
    "\n",
    "\n",
    "for s in all_adjustment_sets:\n",
    "    if all(not t.issubset(s) for t in all_adjustment_sets if t != s):\n",
    "        print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52d7399f",
   "metadata": {},
   "source": [
    "### R Code 6.31\n",
    "\n",
    "Reference: [*Fehiepsi - Numpyro*](https://github.com/fehiepsi/rethinking-numpyro/blob/master/notebooks/06_the_haunted_dag_and_the_causal_terror.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "b6da226b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('M', 'W', {'S'})\n",
      "('W', 'A', {'S'})\n",
      "('S', 'D', {'W', 'A', 'M'})\n"
     ]
    }
   ],
   "source": [
    "all_independencies = dag_6_2.get_all_independence_relationships()\n",
    "\n",
    "for s in all_independencies:\n",
    "    if all(\n",
    "        t[0] != s[0] or t[1] != s[1] or not t[2].issubset(s[2])\n",
    "        for t in all_independencies\n",
    "        if t != s\n",
    "    ):\n",
    "        print(s)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}