Bayesian Thinking

Bayesian communication


Here are some thoughts about the project that my Bayesian students are working on now.

1.  When one communicates a Bayesian analysis, one should clearly state the prior beliefs and the prior distribution that matches these beliefs, the likelihood, and the posterior distribution.

2.  In any problem, there are particular inferential questions, and a Bayesian report should give the summaries of the posterior that answer the inferential questions.

3.  In the project, the questions are to compare two proportions, and if it is reasonable to assume that the proportions are equal.   (The first question is an estimation problem and the second question relates to the choice of model.)

4.  What role does the informative prior play in the final inference?  In the project, the students perform two analyses, one with an informative prior and one with a vague prior.  By comparing the two posterior inferences, one can better understand the influence of the prior information.

5.  There is a computational aspect involved in obtaining the posterior distribution.   In a Bayesian report, one can talk about the general algorithms that were used.  But the computational details (like R code) has to be in the background, say in an appendix.

6.  The focus of the project (of course) is the Bayesian analysis.  But it is helpful to contrast the Bayesian analysis with frequentist methods.   The student should think of frequentist methods for estimation and testing and which methods are appropriate for addressing these questions.   In the project drafts, it seemed the weakest part of the draft was the description of the frequentist methods.