Bayesian core. A practical approach to computational statistics. (English) Zbl 1137.62013

Marin, Jean-Michel; Robert, Christian P.

Springer Texts in Statistics. New York, NY: Springer (ISBN 978-0-387-38979-0/hbk). xiii, 255 p. (2007).

The book is a good, compact and self-contained introduction to the applications of Bayesian statistics and to the use of R to implement the procedures. After a brief introduction to R, Bayesian ideas are introduced in a straightforward way in Chapter 2. The advantage is that the presentation is very dense and quick (no beating around the bush, no preaching on the virtues of Bayesianism), although a bit hard to follow for complete new-comers. On the other hand, a reader with a previous formal course in statistics will enjoy reading this book.
Applications are presented in the following progression: linear models, generalized linear models, capture-recapture experiments, mixture models, dynamic models, image analysis. The topics are therefore a mixture of what every applied researcher should know and some more original choices.
Particular attention is devoted to the use of flat objective priors and a central theme of the book is the use of simulation techniques to explore the posterior distributions of interest. All modern samplers, from the universal Metropolis-Hasting algorithm to the more sophisticated and specific reversible jump MCMC, are explained and illustrated in connection with applications. A good feature of the book is that MCMC techniques are presented not all together, but as the progression into more complex applications requires more complex techniques. As a matter of fact, the authors are not shy of presenting such complex models as hidden Markov models and Markov random fields in a simple and direct way. This adds an edge to a compact and useful text.

Reviewer: Mauro Gasparini (Torino)

MSC:

62F15	Bayesian inference
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
65C60	Computational problems in statistics (MSC2010)
62M99	Inference from stochastic processes
62J12	Generalized linear models (logistic models)
62-04	Software, source code, etc. for problems pertaining to statistics

Keywords:

MCMC simulation; GLM; capture-recapture; mixture models; dynamic models; image analysis

Software:

R