Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. Early chapters present the basic tenets of Bayesian thinking by use of familiar one and two-parameter inferential problems. Bayesian computational methods such as Laplace's method, rejection sampling, and the SIR algorithm are illustrated in the context of a random effects model. The construction and implementation of Markov Chain Monte Carlo (MCMC) methods is introduced. These simulation-based algorithms are implemented for a variety of Bayesian applications such as normal and binary response regression, hierarchical modeling, order-restricted inference, and robust modeling.
Jim Albert is a Distinguished University Professor of Statistics at Bowling Green State University. His research interests include Bayesian modeling and applications of statistical thinking in sports. He has authored or coauthored several books including Ordinal Data Modeling, Bayesian Computation with R, and Workshop Statistics: Discovery with Data, A Bayesian Approach.
An excellent first five chapters which are pretty well documented and have nice code that works at his website. From there the quality is widely considered to drop off. I personally found the exercises a good way to learn basic things about the techniques and trade-offs involved in sampling from multivariate probability distributions.
A well written guide to Bayesian R computation, one thing which really bugged me was the fact that the list of commands were given at the end of each chapter thus it can be confusing at first because we are not told what the commands are meant to do. A lot of the ideas could also be elaborated more too.