Bayesian Core: A Practical Approach to Computational Bayesian Statistics. Jean-Michel MARIN and Christian P. ROBERT. New York: Springer, 2007. ISBN 978-0-387-38979-0. xiii +255 pp. $74.95, GB £ 46.00, 64.15 euros.

Wolfgang Polasek

Recent times have seen several new books introducing Bayesian computing. This book is an introduction on a higher level. “The purpose of this book is to provide a self-contained entry to practical & computational Bayesian Statistics using generic examples from the most common models.”

Yes and no: the purpose is to introduce jointly Bayesian statistics and its computational tools. We thus aim at self-contained-ness, as indicated in the quote. The review seems to question the purpose of the book as well as the intended audience...

The contents of the book is as follows:
  1. Introductory chapter.
  2. Normal models: Conditional distributions, priors, posteriors, improper priors,conjugate priors, exponential families, tests, Bayes factors, decision theory, importance sampling.
  3. Regression and variable selection: G-priors, non-informative priors, Gibbs sampling, variable selection.
  4. Generalised linear models: Probit, logit and log–linear models, Metropolis Hastings algorithms, model choice.
  5. Capture–recapture experiments: Sampling models, open populations, accept-reject algorithm, Arnason–Schwarz model.
  6. Mixture models: Completion, variable dimensional models, label switching, tempering, reversible jump MCMC.
  7. Dynamic models: AR,MA and ARMAmodels, state-space representation, hidden Markov models, forward–backward algorithm.
  8. Image analysis: k-nearest-neighbour, supervised classification, segmentation, Markov random fields, Potts models.
The authors recommend this book for a class of about 7 blocks or “roughly 12–14 weeks of teaching (with 3 h of lectures per week), depending on the intended level and the prerequisites imposed on the students.” In my opinion this is feasible only for mathematics students with a fairly advanced background in statistics.

We [and others] have been teaching from this book for more than three years and the outcome varies quite a lot. We acknowledge that the book cannot be covered in one semester for an undergrad audience, but if computer R labs are added to the three hours of lectures, graduates (with a proper math background, indeed) can achieve a complete picture. Again, there is variability across countries and backgrounds...

The nice thing about the book are the data sets and the R programs that can be downloaded from the authors’ website: In addition, a solution manual with solutions to all exercises is available on the Springer webpage (, but only for instructors.

The book will not be easy to use as a stand-alone textbook, and should be used together with other introductory textbooks (see Bibliography).

This recommendation somehow kills the whole purpose of the book! For instance, the book by Dani Gammerman and Hedibert Lopes somehow covers very similar grounds [maybe at a slightly more advanced level?] and it would not make much sense to have students using both books together. The MCMC book with George Casella is a reference book, so using Bayesian Core in addition does not make sense either, especially because the audience cannot be the same: we are primarily aiming at those students who have had no previous [real] exposure to computational methods and/or Bayesian inference and whose goal is to develop a practical feeling about them. So they can be majoring in other fields, like Economics or Biology with a minor study in Statistics. E.g., our initial cohort of students in Paris was in a professional degree in statistical and financial engineering.

Furthermore, the notation does not follow the mainstream Bayes papers, at least not in Econometrics. A table of abbreviations would have helped. The extensive use of g-priors is surprising, especially in the context of Gibbs sampling, since MCMC should be used to overcome such “convenient” assumptions for priors.

This is more a matter of taste than of usage since the notations are the same as in Monte Carlo Statistical Methods and in The Bayesian Choice. If the notations are different in Econometrics, we are unaware of this fact (and this is the first time we get a complaint about notations.) A table of distributions and of common terms would be useful indeed and can be incorporated in the next edition. As for the choice of the g-priors, there is again a misunderstanding about the purpose of the book: we are quite aware that alternatives can be used for modelling prior information in regression models, but we want to give the student an effective tool by the end of the chapter and g-priors are such tools, especially when using our non-informative version! This point is stressed several times: Bayesian experts will find our choices restrictive and rightly so, but making firm choices about our prior distributions is the only way to achieve an operational tool in 240 pages.

The main recent use of Bayesian model averaging (BMA) is not mentioned, but the reversible jump algorithm is briefly described. Special features of the book are the chapters on capture–recapture models and image analysis.With 240 pages it only scratches on some important topics in Bayesian modelling and the reader has to make up for the “missing links” either by solving the exercises or looking up other books and papers: Unfortunately the reference list could have been much more extensive for this purpose.

Same thing: we deliberately kept the reference list to a minimum, in order to avoid confusing the students. If they want to pursue studies in Bayesian inference, we provide the major textbooks in the area. Journal papers are not appropriate for a crash course, since it is unrealistic to expect students to work on practical implementation and to peruse research papers. In a sense the reference list is already too long! As for solving the exercises, as explained in the User's Manual, they are essential for the comprehension of the book, which means that they must be solved as they come! There are certainly many missing topics for the mature statisticians [and we plan to expand on at least two more chapters in the coming second edition!], but this cannot be avoided in a one-semester course.

Many researchers and Ph.D. students will find the R programs in the book a nice start for their own problems and an innovative source for further developments.

Gamerman D, Lopes HF (2006) Markov chain Monte Carlo: stochastic simulation for Bayesian inference. Texts in statistical science series, 2nd edn. Springer, New York.
Geweke JF (2005) Contemporary Bayesian econometrics and statistics. Wiley, New York
Geweke J, Groenen PJF, Paap R, van Dijk HK (2007) Computational techniques for applied econometric analysis of macroeconomic and financial processes. Comput Stat Data Anal 51(7):3506–3508
Robert CP, Casella G (2004) Monte Carlo statistical methods. Springer texts in statistics, 2nd edn. Springer, New York.