As a starting point, I'd add Doing Bayesian Data Analysis by John Kruschke and Bayesian Computation with R by Jim Albert to the list.

I have read parts of all the books mentioned here. (I teach myself through these texts, and I am a slow learner. So take my comments in that vein.) First, I found that each helped in their own way. I read Jackman's text following Gill's (or I should say that I picked up Jackman's text after I got stuck someplace in Gill's -- which I consulted after getting stuck in Peter Hoff's "A First Course in Bayesian Statistical Methods". Because I was learning more with each attempt, each "next" text seemed better than the previous text. However I will add a few additional books that I have found more pragmatic (from an auto-didactic sense). (By the way - I second the vote for Kruschke. A great book for the beginner Bayesian)

First, as a practical, hands-on, learn-as-you-go text, I do not think you can beat Kery's "Introduction to WinBUGS for Ecologists". It may be aimed at Ecologists - but it walks through modelling syntax basics and then T-Tests, ANOVA, Regression, ANCOVA, Linear Mixed Models and more. It is a hand holding, supportive tutorial that can take a R & WinBUGS novice on a successful Bayesian learning journey. (Kery and co-authour M. Schaub have a follow-on text - but you mus ingest the first before you are ready for the second. However, the second gives a hand-holding tutorial approach which should assist anyone struggling with Part 2 (Multilevel regression) of Gelman and Hill.

The next step after (or co-step with) Kery is - to me - Ioannis Ntzoufras' text "Bayesian Modeling Using WinBUGS. This again can be used by the self-learner. His well commented R-Code can get you into some simple roll-your-own MCMC and Gibbs sampling and his tutorial-like handling of WinBUGS in the raw and through R2WinBUGS is, I think, the best.

If, like me, you need to get more assistance with Gibbs Sampling and MCMC, you should check out "introduction to Probability Simulation and Gibbs Sampling with R" by Suess and Trumbo (you will eat up Albert's book faster if you do) and then onto Robert and Casella's "Introducing Monte Carlo Methods with R".

Now for my surprise suggestion - and one you should really take seriously -- is take a look at Phillip Wordwards "Bayesian Analysis Made Simple". Do not let the sub title mislead you "An Excel GUI for WinBUGS". True, the book explains the use of Phil's Excel interface for WinBugs - but the incredible value of Phil's book is his walk through of the many and divers examples to which he applies his VBA-based GUI in Excel. He explains so much of what others leave out or pass by in doing actual, applied, realistic Bayesian analysis using MCMC and Gibbs Sampling (WinBUGS). Yes, the examples are largely from the medical field (as are Kery's from Ecology) -- but this only adds some inter-disciplinary spice to what is an incredible feast of applied Bayesian Analysis.

Last but not least, I will add the works of two more "schools/authors". The first is work of William Bolstad. His is a statistical-computational approach. His "Introduction to Bayesian Statistics" simply assumes that you will do inferential statistics as a Bayesian and his "computational Bayesian Statistics" teaches you how.

The second is the work by Alan Zuur and his associates. Mostly they are solid, traditional "Frequentists" (I dislike this term, but you know what I mean, and I myself am such a Frequentist). But they offer a great insight into "zero-inflated" models and Bayesian techniques in their most recent publication "Zero Inflated Models and Generalized Linear Mixed Models with R". Again, the subject matter is Ecology, but....

George,

Many thanks for posting your reply on resources for Bayes beginners. Like you I am finding that one book is not enough. My current book by Kruschke is good but has me asking questions. I need to step back and try something else, perhaps Kery's book for ecologists.

Sincerely,

Davester