I've got exactly the same feeling. Could you suggest a good introductory textbook into MCMC? They left it as a mysterious blackbox and I'm not very uncomfortable with using mathematical blackboxes I don't understand.
They are covered near the end of the book. It should be enough to familarize yourself with and understand the basic concepts of MCMC. Anything more in-depth will require a strong mathematical background.
BTW : There are probably a ton of books that cover MCMC out there - that's just one I liked and which is freely downloadable.
I have some background (grad student in cfd, thinking about switching to some sort of data analysis later on) but my measure theory and probability skills are rusty (on the other hand numerical linear algebra, functional calculus and complex analysis are superb). What would be a good book for my level?
http://www.amazon.com/Data-Analysis-Bayesian-Tutorial-Public... is short and reputable on Bayesian statistics. On MCMC specifically, I don't know, but MCMC is really a kind of algorithm that lets you find the answer to a mathematical question (so I think understanding the math is the right thing to start with).
PS. There a second edition of that book, but I've heard that the first edition is better, because the second edition added a different author and expanded the book.
They are covered near the end of the book. It should be enough to familarize yourself with and understand the basic concepts of MCMC. Anything more in-depth will require a strong mathematical background.
BTW : There are probably a ton of books that cover MCMC out there - that's just one I liked and which is freely downloadable.