MARIN, J. M. and ROBERT, C. P. Bayesian Core: A Practical Approach to Computational Bayesian Statistics. Springer, New York, 2007. xiv+258 pp. US$74.95/€64.15, ISBN 0-387-38979-0.

It is by now an overworked cliché (and even a cliché to call it a cliché!) that the rise in practical application of Bayesian methods was precipitated by the advent of fast computers and accompanying computational algorithms. While a number of books have presented Bayesian methods and the accompanying technology to a wider audience, these have often either been for beginners only (Berry, 1996; Lee, 1997; Woodworth, 2004), lacked sufficient computational details for real practice (Berry and Stangl, 1996; Gelman et al., 2003), focused on just one computational technique (Gilks, Richardson, and Spiegelhalter, 1996; Congdon, 2001, 2003), or lacked realistic examples of data analyses (Bernardo and Smith, 1994; O’Hagan, 1994; Chen, Shao, and Ibrahim, 2000; Evans and Swartz, 2000; Tanner, 2002). Therefore, despite the plethora of Bayesian materials now available, there remains room for a book aimed at exposing both the theory and practice of a variety of computational algorithms within the context of real examples. According to the preface of “Bayesian Core,” the book provides a “self-contained entry into practical and computational Bayesian statistics” with “its primary audience consisting of graduate students who need to use (Bayesian) statistics as a tool to analyze their databases.” They also claim that the “book should appeal to scientists in all fields.” It is perhaps quixotic to hope to explain complex numerical algorithms to nonstatistician scientists in a book only 246 pages long, while also providing sufficient detail to satisfy graduate statistics students, so it is not surprising that the book is only partially successful in attaining its stated goals.

Structurally, the book consists of eight chapters: The introductory chapter explains the scope of the book, and introduces R as a programming language. Chapter 2 covers simple normal models, taking the opportunity to introduce basics of Bayesian analysis, including prior distributions, credible intervals (which the authors call confidence intervals, despite the Bayesian orientation of the book), testing, and simple Monte Carlo methods, including importance sampling. Linear regression with variable selection is covered in Chapter 3, followed by a chapter on generalized linear models. It is within these two chapters that MCMC methods are introduced. Chapter 5 is wholly devoted to capture–recapture models, and the next two chapters discuss mixture models (including label switching difficulties and reversible jump MCMC) and dynamic models (including AR, MA, ARMA, and hidden Markov models). The final chapter is on image analysis, including Markov random fields.

Data sets and R programs are available on the book’s website. The matching of each computational technique to a real data set allows readers to fully appreciate the Bayesian analysis process, from model formation to prior selection and practical implementation. The sections in Chapter 3 discussing the various types of priors (Jeffrey’s, G-priors) available for linear regression models are useful. The pitfalls of straightforward Gibbs sampling are well illustrated through examples,and alternatives with better properties are given. The idea to mix R programs with the algorithms is a good one, but only partially realized. Past the very brief introduction in Chapter 1, no R programs are given in the text, and those on the website are largely uncommented and not that easy to follow. On the other hand, descriptions of some techniques such as the accept/reject algorithm in Chapter 5 are nice.

We agree that more R code could have been included in the book and we contemplate including most R codes in the second edition of the book. Our reluctance to do so in the first edition was due to the fact that, as the complexity of the topic increases, so does the length of the R code and thus the difficulty of commenting it.

This book is not without its idiosyncrasies. It becomes clear early on that this is not an ideal book for self-study, nor would it be appropriate for scientists without an undergraduate degree in mathematical statistics. The minimal background is a course at the level of Casella and Berger (2001). For example, exercise 1.1 on page 3 requires an understanding of Lebesgue measure, and exercise 2.1 on page 15 suggests computing the first four moments of the normal density. Self-study is limited by crucial material being included only as exercises, with no solutions given, either in the book or on the website. This also severely restricts the book’s usefulness as a reference text. For example, the formula for the posterior confidence interval for a linear regression coefficient is given only as exercise 3.5.

The book was designed as a textbook for undergraduate and/or graduate students and therefore it somehow rules out self-study except for most advanced or mature students. This is also the reason why solutions to the exercises are not provided, except for instructors on Springer's website. When CPR taught from the book in New-Zealand, the third year [math & stat) students who took the course managed to solve the exercises despite a limited probabilistic background. The reference to the Lebesgue measure in Exercise 1.1 is akward and unnecessary, and it should vanish from the second edition. Same thing for Exercise 2.1. A good knowledge of Riemann integration is however necessary to handle Bayesian computations: this is unavoidable. So we agree that some prior exposure to probability theory and to mathematical statistics is appropriate, even though a complete coverage of Casella and Berger (2001) is not necessary.

There is an admittedly “rather sketchy” selection of topics. For example, a whole chapter is devoted to capture–recapture models, but no examples of simple binomial, difference between two normal means, or two by two table models.

The motivation for the topics was to get into the major aspects of Bayesian Statistics through datasets (and models) that would reflect the variety of the applications of Bayesian Statistics. While capture-recapture may appear as an over-specialised topic (and this was also stressed in earlier reviews), we think it is a good motivating entry to (a) ecological data, (b) discrete sampling models, (c) longitudinal data, (d) missing variables, and (e) hidden Markov models. The very beginning of Chapter 5 deals with the simple binomial model, while Chapter 4 ends up with contingency tables. Obviously, there will always be important models that are not covered in a 246 page book and we had no intention to be exhaustive. The second edition may include one or two more chapters, maybe covering meta-analysis and hierachical models, but even such an addition cannot fully answer the criticism...

Loss functions are casually tossed into a paragraph on page 20 with no formal introduction or further discussion. On page 80, the authors express surprise that the “frequentist” BIC criterion provides similar model selection results compared to Bayes’ factors, never mentioning the close Bayesian connection between these two criteria (Raftery, 1999).
The decision-theoretic motivations for using Bayesian Statistics are obviously essential and this is the theme underlying The Bayesian Choice. However, this book is primarily intended for (future) practical implementations of Bayesian Statistics, and the use of loss functions is marginal in most studies. With more space, we could address realistic loss problems, including Bayesian design or multiple comparisons, but we had to make choices. The comment on BIC is intended for our students, who may have encountered BIC as a black-box alternative to AIC, not for specialists of the field, and we think that exposing the connection would have taken too much time, while being (a) too advanced for most students and (b) not completely convincing. Note that we personally disagree with the use of BIC in a Bayesian framework (see the discussion in The Bayesian Choice, second edition).

There are also some typographical errors. For example, the website given for downloading the R software on page 6 is incorrect, as is the definition of log odds on page 89.

There are indeed many typos, for which we apologise, and we are very grateful to all readers, including the reviewer, for pointing them out. A first batch [listed on the webpage] was corrected for the second printing of the first edition and we are now keeping track [see webpage] of additional typos for the third printing.

Overall, a book such as Gelman et al. (2003) may be preferred for a first course in Bayesian data analysis, and Tanner (2002) is more comprehensive in its coverage of computational issues. Nevertheless, this book might be considered for a course that combines these two topics, especially with a good instructor to guide students through the rougher parts. A second edition that corrects typographical errors (the two listed above are not yet acknowledged on the book’s website), includes solutions to exercises at the back of the book, and provides better commented R programs to fully illustrate each algorithm may enable a wider audience.

Thanks for the suggestions: we will indeed increase the coverage of R in the second edition, without hopefully introducing new typos! For the reason mentioned above, we cannot make solutions to exercises available for students. And we completely agree that the book requires a good instructor to be taught from, hoping that the availability of slides, R codes, and latex files will help those teaching from the book. The comparison with Gelman et al. (2003) and Tanner (2002) is delicate to discuss, but we feel that Bayesian Core provides a more realistic understanding of Bayesian data analysis, thanks to the constant reference to a supporting dataset and to a more directive discussion on the choice of prior distributions. 


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Lawrence Joseph
Department of Epidemiology and Biostatistics
McGill University
Montréal, Québéc, Canada