I have reviewed a number of statistics texts for academic journals over the years, and have authored published reviews of some six books specifically devoted to Bayesian analysis. I consider John Kruschke's "Doing Bayesian Data Analysis" to be the best text available for learning this branch of statistics.Thank you, Joe!
Learning how to craft meaningful statistical tests and models based on Bayesian methods is not an easy task. Nor is it an easy task to write a comprehensive basic text on the subject -- one that actually guides the reader through the various Bayesian concepts and mathematical operations so that they have a solid working ability to develop their own Bayesian-based analyses.
There are now quite a few texts to choose from in this area, and some are quite good. But Kruschke's text, in my opinion, is the most useful one available. It is very well written, the concepts unique to the Bayesian approach are clearly presented, and there is an excellent instructors manual for professors who have adopted the book for their classes. Kruschke uses R and WinBUGS for showing examples of the methods he describes, and provides all of the code so that the reader can adapt the methods for their own projects.
"Doing Bayesian Data Analysis" is not just an excellent text for the classroom, but also -- and I think foremost -- it is just the text one would want to work through in order to learn how to employ Bayesian methods for oneself.
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