In this post, I’d like to lay out a few questions and concerns I have about Bayesianism and Bayesian decision theory as a normative theory of inductive inference. As a positive theory, of what people do, psychology is full of demonstrations of cases where people do not use Bayesian reasoning (the entire “heuristics and biases” area), which is interesting but not my target. There are no new ideas here, just a summary of some old concerns which merit more consideration, and not even necessarily the most important ones, which are better covered elsewhere.
Prompted by a question on the slack for Turing.jl about when to use which Bayesian sampling algorithms for which kinds of problems, I compiled a quick off-the-cuff summary of my opinions on specific samplers and how and when to use them. Take these with a grain of salt, as I have more experience with some than with others, and in any case the nice thing about a framework like Turing is that you can switch out samplers easily and test for yourself which is best for your application.