This book’s title captures its focus. It is a textbook covering the core statistical models from both a Bayesian viewpoint and a computational viewpoint. The book’s structure is similar for each core model covered. There is a discussion of the choice of priors, along with math to derive the priors. There is a discussion of the computational problem, with algorithms given. This material is covered in the context of example datasets and example R code.

The book is being actively used as a textbook by a number of university courses. Its Web site includes lecture slides, the R code, and errata (http://www.ceremade.dauphine.fr/~xian/BCS/).

The course level is graduate or advanced undergraduate. Solutions to the exercises are available to course instructors, from the publisher.

The book is pleasingly short. To keep the punchy focus, Marin and Robert expressly avoid survey material such as historical developments or descriptions of endless minor variations of models. Even more unusual for a Bayesian text, the authors avoid giving justifications or motivations for the Bayesian approach versus other approaches; I found this remarkably refreshing. As someone who practices within a Bayesian framework, I appreciate being able to get straight to the data, models, and computations.

The core models covered by Bayesian core are: normal models, regression models, generalized linear models, capture-recapture models, mixture models, time series with hidden Markov models, and image analysis. The core algorithms used to estimate the models are: Monte Carlo, Markov chain Monte Carlo (MCMC), Metropolis-Hastings, and the Gibbs sampler. (On the book’s Web site, Marin and Robert have noted that a second edition may include hierarchical models and meta-analysis.) The book’s coverage of the key models is good.

I really like the writing style. Good intuition is provided behind the algorithms. A good example of the style is the discussion of the reversible jump MCMC models in the context of mixture models in chapter 6 and time series AR(p) models in chapter 7. The book’s use of datasets and code is still relatively rare for a statistical textbook. The authors note that statistical practice is a combination of math, data analysis, and computation. It can only help the training of good practitioners to have textbooks covering these three facets.

The authors slightly overstate a claim, in the preface, that the book has an emphasis on “practice”--or I might have a different understanding of practice. The practice in Bayesian core is practice in the context of a course’s laboratory practicals, but it is not practice in the context of professional consulting practice. If the intent is to cover more of the consulting case study angle, the running examples could be extended to consider the real-world problem being addressed, and the why and how of data collection. There would also be more material on presentation and interpretation of the models and linking this to the problem’s solution. The book’s running examples provide data on which to compute models, rather than problems for which data needs to be collected and models used to solve the problem. The book does not provide a problem-solving sense of “discovery.” Instead, I got a sense of discovery from the book’s explanation of the reasoning behind certain priors and the computational methods to estimate a posterior distribution.

In conclusion, the book does what it does well. Fuller case studies of data analysis with Bayesian models can be found elsewhere [1,2].