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This is a very well written text that is a particularly good reference on algorithms for the professional statistician. A nice feature is that it is concise and yet thorough. Many important problems in statistics are covered and presented through the deterministic and Monte Carlo techniques. Topics covered include the item response model, missing data and Bayesian methods. Most algorithms used to find maxima of posterior distributions can also be employed for maximizing likelihood. So those preferring classical inference can get a lot out of this book as well as the Bayesians.
The orientation is toward the Bayesian approach however, with good coverage of prior and posterior distributions, conjugate priors and Bayesian Hierarchical Models. The last chapter on Markov Chain Monte Carlo methods is mostly used for Bayesian inference.
This is a great reference source but can also be used in a graduate level course on mathematical statistics, probably as a supplemental text. There are many useful exercises in this edition. The book is fairly advanced and presupposes an introduction to mathematical statistics at the level of the text by Bickel and Doksum. It also assumes that the reader has had some introduction to Bayesian methods but only at the level of, say, Box and Tiao's text. It does not assume any knowledge of stochastic processes including Markov chains.
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