Any good book reccomendations for Baysian statistics, discrete choice models, experimental design, stochastic?

Question

Any good book reccomendations for Baysian statistics, discrete choice models, experimental design, stochastic differential equations, or artificial intelligence that have a more rigorous footing?

Answer 1

A really good book is Bayesian Data Analysis, Second Edition, by Andrew Gelman, et al. I found it to be one of the easier to comprehend books on Bayesian statistics. It was as "rigorous" as you might like, but I have found it absolutely useful in day to day analysis tasks.

However, I have to admit that until I had a formal course in Bayesian Statistics, reading all the books I tried to read on the subject just didn't get to the fundamental gist. David Draper out of the University of California, Santa Cruz is about one of the best mathematics / statistics lecturers I've ever encountered. He put together the foundation that helped me understand the Gelman work. But reading Gelman first helped me appreciate what I was learning from Draper. If Draper ever finishes his book (the basis for the course notes), I'd recommend that as a good foundation for more rigorous understanding.

Answer 2

Not books, but two good articles on the web:

An Intuitive Explanation of Bayesian Reasoning
By Eliezer Yudkowsky
http://yudkowsky.net/bayes/bayes.html

A Technical Explanation of Technical Explanation
©2005 by Eliezer Yudkowsky.
http://yudkowsky.net/bayes/technical.html