Jouni pointed me to this forthcoming book by Jim Albert. Here are the table of contents:
An introduction to R.- Introduction to Bayesian thinking.- Single parameter models.- Multiparameter models.- Introduction to Bayesian computation.- Markov chain Monte Carlo methods.- Hierarchical modeling.- Model comparision.- Regression models.- Gibbs sampling.- Using R to interface with WinBUGS.
At 280 pages, Jim’s book looks like it will be a great place for people to get started.
I’ll also recommend Appendix C of BDA, where we get you started and work through a basic hierarchical model in R/Bugs and then program it in R alone. In doing these, we work through different parameterizations of the model.
P.S. In the first version of this blog entry I’d judged the contents of the book too quickly. Jim Albert sent me more info:
Since I saw your mention of my book on your blog, I thought I should address your worries.
First, I actually discuss Gibbs sampling pretty early in the book. Chapters 5 and 6 talk about a lot of Bayesian computational issues and I describe Gibbs sampling and the generic Metropolis within Gibbs algorithm that can be used for an arbitrary real-valued posterior. Chapter 10 describes a few more sophisticated models that are well fit by Gibbs sampling.
Second, model checking appears throughout the book. Early on, I talk about the use of the prior predictive to check the suitability of a Gamma prior for a Poisson problem. In the regression and hierarchical modeling chapters, I apply posterior predictive checking. In Chapter 7, I talk about more formal Bayesian model checking by Bayes factors.
I view my book as a suitable companion book for an introductory Bayesian course; in fact, I thought of Gelman et al as maybe the most likely book that my book would work for.
I’m sure that many Bayesians would write different R books depending on their background and preferences, but my book is a good reflection of what I do in my Bowling Green course.
Another book which is quite good for Bayesian computation in R is "Bayesian Core" by Marin and Robert. There is a large bank of accompanying R code on the book's website.
I followed the link and looked at the contents to the Marin and Robert book. They didn't seem to have hierarchical models, which surprised me. In that case, their book is entirely complementary to my Appendix C of BDA!