I am in the market for a textbook that explains Bayesian methods for non-parametric tests. My experience with Bayesian statistics thus far comes from John Krushke’s Doing Bayesian Data Analysis, but this book excludes non-parametric statistics. I do see that your text, Bayesian Data Analysis 3e, covers non-parametric statistics, however, does it contain instructions on how to conduct Bayesian alternatives to things such as the Mann-Whitney U Test, Kruskal-Wallis, etc specifically? I’m fairly statistics naive, being mostly self-taught, and am admittedly only recently aware of what non-parametric tests are. I’m currently a master’s student, and have taken a great liking to statistics, especially Bayesian methods, and am keen to learn more.
My reply: I don’t think you need to do Mann-Whitney U Test, Kruskal-Wallis, etc. In BDA we briefly explain why we don’t do the Wilcoxon (see post here), and I think the same reasoning goes for these other tests. Just model what you want to model directly, and forget about the whole null hypothesis significance testing thing.