Updating raven

Author: AllenDowney

examples/raven.ipynb

@@ -1824,14 +1824,27 @@
     "Response: Yes, Bayesian analysis is subjective, but only partly because of priors. It is also subjective because is it based on a model of the data generating process, and model selection is subjective. So avoiding priors is pointless: it limits what you can do without actually eliminating subjectivity."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "7dc7d21d",
+   "metadata": {},
+   "source": [
+    "Objection: [From a correspondent](https://github.com/AllenDowney/ThinkBayes2/issues/83): \"The standard Bayesian solution posits a fixed number of ravens, non-ravens, and black objects and concludes correctly that a randomly sampled non-black non-raven sighting does change (slightly) the probability that all ravens are black (since that slightly increases the probability that the remaining objects, including all the ravens, are black).\"\n",
+    "\n",
+    "Response: Yes, there are other models of Scenario 2 where a non-black non-raven is evidence for `A`. I think that supports my claim that the conclusion depends on our model of the data-generating process. I won't argue that my model is right -- only that it is one example of a model where the conclusion is consistent with intuition."
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "c12912fd",
    "metadata": {},
    "source": [
     "Objection: The finite-world model assumes we know the total number of ravens and non-ravens (`N` and `M`). That's unrealistic.\n",
     "\n",
-    "Response: The values of `N` and `M` are not essential to the argument. They simply instantiate the logic in a finite world where computing likelihoods is tractable. If `N` and `M` are unknown, we can extend the model by assigning priors to them as well. The qualitative result still holds: Scenario 2 provides no information about `A` because its likelihood is independent of `i`, while Scenario 4’s likelihood depends on both `i` and `j`. The paradox arises from the sampling structure, not from the population sizes."
+    "Response: I agree that it's unrealistic for the raven example. But I think it's a useful modeling strategy to treat them as known quantities and then see what happens as they get bigger. \n",
+    "An alternative is to treat `N` and `M` as unknown, assign priors, and update them along with `i` and `j`.\n",
+    "I haven't done that analysis, but I think in that case a non-black non-raven might or might not be evidence for `A`, depending on the priors.\n",
+    "Again, this supports my claim that the conclusion depends on our model of the data-generating process, including the priors."
    ]
   },
   {