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‎dist/Contents.m

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% PROBABILITY DISTRIBUTION FUNCTIONS (contents of the dist-folder):
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%
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% probability density functions
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% BETA_LPDF - Beta log-probability density function (lpdf).
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% BETA_PDF - Beta probability density function (pdf).
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% DIR_LPDF - Log probability density function of uniform Dirichlet
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% distribution
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% DIR_PDF - Probability density function of uniform Dirichlet
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% distribution
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% GAM_CDF - Cumulative of Gamma probability density function (cdf).
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% GAM_LPDF - Log of Gamma probability density function (lpdf).
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% GAM_PDF - Gamma probability density function (pdf).
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% INVGAM_LPDF - Inverse-Gamma log probability density function.
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% INVGAM_PDF - Inverse-Gamma probability density function.
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% LAPLACE_LPDF - Laplace log-probability density function (lpdf).
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% LAPLACE_PDF - Laplace probability density function (pdf).
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% LOGN_LPDF - Log normal log-probability density function (lpdf)
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% LOGT_LPDF - Log probability density function (lpdf) for log Student's T
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% MNORM_LPDF - Multivariate-Normal log-probability density function (lpdf).
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% MNORM_PDF - Multivariate-Normal log-probability density function (lpdf).
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% KERNELP - Kernel density estimator for one dimensional distribution.
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% NORM_LPDF - Normal log-probability density function (lpdf).
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% NORM_PDF - Normal probability density function (pdf).
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% POISS_LPDF - Poisson log-probability density function.
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% POISS_PDF - Poisson probability density function.
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% SINVCHI2_LPDF - Scaled inverse-chi log-probability density function.
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% SINVCHI2_PDF - Scaled inverse-chi probability density function.
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% T_LPDF - Student's T log-probability density function (lpdf)
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% T_PDF - Student's T probability density function (pdf)
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% NORM_P - create Gaussian (multivariate) (hierarchical) prior
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% INVGAM_P - Create inverse-Gamma prior
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%
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% Error and gradient functions:
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% INVGAM_E - compute an error term for a parameter with inverse
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% gamma distribution (single parameter).
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% INVGAM_G - compute a gradient term for a parameter with inverse
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% gamma distribution (single parameter).
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% LAPLACE_E - compute an error term for a parameter with Laplace
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% distribution (single parameter).
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% LAPLACE_G - compute a gradient for a parameter with Laplace
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% distribution (single parameter).
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% MNORM_E - compute an error term for parameters with normal
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% distribution (multiple parameters).
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% MNORM_G - compute a gradient for parameters with normal
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% distribution (multible parameters)
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% MNORM_S - Maximum log likelihood second derivatives
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% NORM_E - compute an error term for a parameter with normal
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% distribution (single parameter).
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% NORM_G - compute a gradient for a parameter with normal
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% distribution (single parameter).
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% NORM_S - Maximum log likelihood second derivatives (single variable)
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% T_E - compute an error term for a parameter with Student's
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% t-distribution (single parameter).
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% T_G - compute a gradient for a parameter with Student's
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% t-distribution (single parameter).
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% DIR_E - compute an error term for a parameter with Dirichlet
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% distribution (single parameter).
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% GINVGAM_E - Compute an error term for a parameter with inverse
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% gamma distribution (single parameter).
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% GINVGAM_G - Compute a gradient term for a parameter with inverse
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% gamma distribution (single parameter).
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% GP2R_E - Evaluate error function for Gaussian Process.
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% GP2R_G - Evaluate gradient of error for Gaussian Process.
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% GNORM_E - Compute an error term for a parameter with normal
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% distribution (single parameter).
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% GNORM_G - Compute a gradient for a parameter with normal
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% distribution (single parameter).
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% GNORM_S - Maximum log likelihood second derivatives.
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% GT_E - Compute an error term for a parameter with Student's
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% t-distribution (single parameter).
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% GT_G - Compute a gradient for a parameter with Student's
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% t-distribution (single parameter).
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% GT_S - Maximum log likelihood second derivatives for
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% t-distribution.
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% T_S - Maximum log likelihood second derivatives for t-distribution
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% T_P - Create student t prior
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%
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% Functions to sample from full conditional distribution
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% COND_GINVGAM_CAT - Sample conditional distribution from
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% inverse gamma likelihood for a group and
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% categorical prior.
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% COND_GNORM_INVGAM - Sample conditional distribution from
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% normal likelihood for group and
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% inverse gamma prior.
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% COND_GNORM_NORM - Sample conditional distribution from normal
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% likelihood for a group and normal prior.
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% COND_GT_CAT - Sample conditional distribution from t
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% likelihood for a group and categorical prior.
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% COND_GT_INVGAM - Sample conditional distribution from t
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% likelihood for a group and inverse gamma prior.
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% COND_INVGAM_CAT - Sample conditional distribution from
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% inverse gamma likelihood and categorical prior.
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% COND_INVGAM_INVGAM - Sample conditional distribution from
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% inverse gamma likelihood and prior
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% COND_LAPLACE_INVGAM - Sample conditional distribution from Laplace
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% likelihood and inverse gamma prior.
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% COND_MNORM_INVWISH - Sample conditional distribution from normal
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% likelihood for multiparameter group and
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% inverse wishard prior.
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% COND_NORM_GINVGAM - Sample conditional distribution from
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% normal likelihood and inverse gamma prior
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% for a group
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% COND_NORM_INVGAM - Sample conditional distribution from
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% normal likelihood and inverse gamma prior
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% COND_T_CAT - Sample conditional distribution from t
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% likelihood and categorical prior.
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% COND_T_INVGAM - Sample conditional distribution from t
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% likelihood and inverse gamma prior.
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%
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% Random number generators
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% CATRAND - Random matrices from categorical distribution.
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% DIRRAND - Uniform dirichlet random vectors
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% EXPRAND - Random matrices from exponential distribution.
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% GAMRAND - Random matrices from gamma distribution.
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% INTRAND - Random matrices from uniform integer distribution.
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% INVGAMRAND - Random matrices from inverse gamma distribution
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% INVGAMRAND1 - Random matrices from inverse gamma distribution
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% INVWISHRND - Random matrices from inverse Wishart distribution.
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% NORMLTRAND - Random draws from a left-truncated normal
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% distribution, with mean = mu, variance = sigma2
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% NORMRTRAND - Random draws from a right-truncated normal
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% distribution, with mean = mu, variance = sigma2
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% NORMTRAND - Random draws from a normal truncated to interval
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% NORMTZRAND - Random draws from a normal distribution truncated by zero
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% WISHRND - Random matrices from Wishart distribution.
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% SINVCHI2RAND - Random matrices from scaled inverse-chi distribution
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% TRAND - Random numbers from Student's t-distribution
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% UNIFRAND - Generate unifrom random numberm from interval [A,B]

‎dist/beta_lpdf.m

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function y = beta_lpdf(x,a,b)
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%BETA_LPDF Beta log-probability density function (lpdf).
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%
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% Y = BETA_LPDF(X,A,B) Returns the log of the Beta pdf with
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% parameters A and B, at the values in X.
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%
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% The size of Y is the common size of the input arguments. A scalar input
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% functions as a constant matrix of the same size as the other inputs.
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%
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% Default value for A and B is 1.
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% Copyright (c) 2005 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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if nargin < 3,
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a = 1;
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end
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if nargin < 2;
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b = 1;
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end
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if nargin < 1,
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error('Requires at least one input argument.');
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end
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y= (a-1).*log(x) +(b-1).*log(1-x) -betaln(a,b);

‎dist/beta_pdf.m

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function y = beta_pdf(x,a,b)
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%BETA_PDF Beta probability density function (pdf).
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%
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% Y = BETA_PDF(X,A,B) Returns the Beta pdf with
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% parameters A and B, at the values in X.
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%
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% The size of Y is the common size of the input arguments. A
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% scalar input functions as a constant matrix of the same size as
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% the other inputs.
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%
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% Default value for A and B is 1.
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% Copyright (c) 2005 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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if nargin < 3,
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a = 1;
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end
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if nargin < 2;
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b = 1;
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end
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if nargin < 1,
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error('Requires at least one input argument.');
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end
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y=exp((a-1).*log(x) +(b-1).*log(1-x) -betaln(a,b));

‎dist/catrand.dll

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‎dist/catrand.m

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function r = catrand(p, m, n);
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%CATRAND Random matrices from categorical distribution.
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%
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% Description
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% R = CATRAND(P) returns a matrix of random numbers chosen
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% from the categorical distribution with parameter P.
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% P is array of probabilities, which are not necessarily
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% normalized, though they must be non-negative, and not all zero
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% The size of R is the size of P. Alternatively,
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% R = CATRAND(P,M,N) returns an M by N matrix.
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% Copyright (c) 1999-2004 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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p=p(:);
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pc=cumsum(p);
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pc=pc./pc(end);
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if nargin < 2
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m=1;n=1;
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elseif nargin <3
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n=m;
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end
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r=binsgeq(pc,rand(m,n));

‎dist/catrand.mexaxp

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‎dist/catrand.mexglx

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‎dist/cond_ginvgam_cat.m

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function r = cond_ginvgam_cat(a, a1, a2, x)
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% COND_GINVGAM_CAT Sample conditional distribution from inverse
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% gamma likelihood for a group and categorical prior.
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%
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% Description
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% R = COND_GINVGAM_CAT(A, A1, A2, X) generates one sample
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% from the conditional distribution of A given
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% parameter structure X of lower level, structure A1 of
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% same level hyper-parameters and A2 of higher level, i.e
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% is r~P(A|A1,A2,X). Returns one new sample R from the
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% distribution above.
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% Copyright (c) 1999-2000 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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ii=a1.ii;
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m=length(ii);
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s=a1.s;
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nus=a2.nus;
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p=nus;
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r=zeros(1,m);
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for i=1:m
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xi2=x(ii{i}).^2;
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s2=s(i).^2;
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for j=1:length(nus)
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p(j)=sum(invgam_lpdf(xi2,s2,nus(j)));
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end
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p=exp(p-max(p));
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r(i)=nus(catrand(p));
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end

‎dist/cond_gnorm_invgam.m

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function r = cond_gnorm_invgam(a, a1, a2, x)
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% COND_GNORM_INVGAM Sample conditional distribution from
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% normal likelihood for group and
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% inverse gamma prior.
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%
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% Description
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% R = COND_GNORM_INVGAM(A, A1, A2, X) generates one sample
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% from the conditional distribution of A given
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% parameter structure X of lower level, structure A1 of
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% same level hyper-parameters and A2 of higher level, i.e
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% is r~P(A|A1,A2,X). Returns one new sample R from the
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% distribution above
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% Copyright (c) 1999-2000 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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ii=a1.ii;
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m=length(ii);
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r=zeros(1,m);
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if size(a2.s,2)>1
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for i=1:m
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n=length(ii{i});
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r(i)=sqrt(invgamrand1((a2.nu*a2.s(i).^2+sumsqr(x(ii{i})))/(a2.nu+n), a2.nu+n));
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end
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else
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for i=1:m
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n=length(ii{i});
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r(i)=sqrt(invgamrand1((a2.nu*a2.s.^2+sumsqr(x(ii{i})))/(a2.nu+n), a2.nu+n));
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end
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end

‎dist/cond_gnorm_norm.m

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function r = cond_gnorm_norm(a, a1, a2, x)
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% COND_GNORM_NORM Sample conditional distribution from normal
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% likelihood for a group and normal prior.
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%
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%
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% Description
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% R = COND_GNORM_NORM(A, A1, A2, X) generates one sample
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% from the conditional distribution of A given
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% parameter structure X of lower level, structure A1 of
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% same level hyper-parameters and A2 of higher level, i.e
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% is r~P(A|A1,A2,X). Returns one new sample R from the
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% distribution above.
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% Copyright (c) 1999-2000 Aki Vehtari
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% This software is distributed under the GNU General Public
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% License (version 2 or later); please refer to the file
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% License.txt, included with the software, for details.
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ii=a1.ii;
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m=length(ii);
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if size(a2.s,2)<m
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a2.s=a2.s(ones(1,m));
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end
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r=zeros(1,m);
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for i=1:m
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n=length(ii{i});
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p1=n./a1.s(i).^2;p2=1./a2.s(i).^2;
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r(i)=(p2*a2.mu+p1*mean(x(ii{i})))./(p1+p2)+randn(1)*sqrt(1./(p1+p2));
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end

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