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.

Jarrett J. BARBER

University of Wyoming

New York: Springer, 2007. ISBN 978-0-387-38979-0. xiii +255 pp. $74.95.

As
its title suggests, this text intentionally focuses on a few
fundamental Bayesian statistical models and key computational tools. By
avoiding a more exhaustive coverage of Bayesian statistical and
computational techniques readily found in other texts, the authors have
successfully cultivated an understanding of the process of creating and
implementing a practical Bayesian statistical model for data analysis
from beginning to end or, perhaps better-phrased, from prior to
posterior. The end result is an
exceptionally unique and well integrated “hands-on” treatment of
Bayesian statistical modeling and computational techniques that will whet the dedicated student’s appetite for more complex Bayesian modeling and data analysis.

The
authors’ format is consistent throughout the chapters, leading the
student through an analysis of one or more data sets from beginning to
end. The beginning of each chapter presens the student with a road
map—a sort of annotated table of contents—of chapter topics. (Actually,
the road map is preceded by a figure and a short quotation from books
by Scottish novelist Ian Rankin,
most of which, as the authors acknowledge, usually have little to do
with chapter topics.) Each chapter focuses on one or more data sets
introduced early in the chapter and revisited throughout the text and
the exercises, which are purposefully placed within the text instead of
at the end. This sets the stage for the development and discussion of
appropriate data models, priors, posterior derivations, and
computational techniques. Emphasis is placed on discussion of different
prior distributions, which is appropriate given the text’s applied
nature. The exercises vary in their level of difficulty, perhaps
comparable to that found in the text by Casella and Berger (2002).
Successful completion of the exercises is often necessary for the
reader to fully understand current or subsequent developments in the
text. A wide range of exercise types is included. I was particularly
impressed by the repeated emphasis on posterior propriety. The
foundational topics of Bayes theorem, conjugacy, and Jeffreys’ and
G-priors are introduced within the familiarity of normal models, along
with brief coverage of hypothesis testing, confidence intervals, and
Bayes factors. Other topics include linear models and generalized
linear models—probit, logit, and log-linear—as well as more specialized
introductions to capture–recapture experiments, mixture models, dynamic
models, and models for image analysis.

The
powerful tool of latent variables is a recurring theme. Starting with
the simple-to-understand latent variable representation of the probit
model, the authors illustrate basic interpretive and sampling
advantages of latent variables. With the basic idea established, the
student is prepared to appreciate their power in the Arnason–Schwarz
capture–recapture model wherein, in one example, the location of a
lizard is specified as a partially hidden Markov model. Hidden Markov
models reappear in the chapter on dynamic models. Coverage of latent
variables continues in several other applications, including mixture
models (where they are used to indicate a unit’s unobserved mixture
component), as the state variables in the state-space representation of
dynamic models, and, in the form of auto-logistic priors, Ising and
Potts models (in their application to image segmentation as models for
the underlying “true” image). The authors use Gibbs and
Metropolis–Hastings algorithms throughout, and are careful to tailor
the details of each as they revisit these algorithms with new
applications (e.g., the Arnason–Schwarz capture–recapture Gibbs, the
Potts Metropolis–Hastings). These and other applications gradually
build the students’ confidence for modifying basic off-the-shelf
algorithms for exploring sampling efficiency. Reversible-jump Markov
chain Monte Carlo (RJMCMC) sampling for variable dimension models is
introduced through mixture models with unknown numbers of components,
and RJMCMC is again unsheathed to handle unknown orders in
autoregressive and moving average models. Finally, few students will
want to miss simulated tempering by pumping, which is used to provide extra boosts of energy to move among the hills of the posterior in its application to mixture models.

Bayesian Core is more than a textbook; it is an entire course carefully crafted with the student in mind. It is accompanied by a no-nonsense website providing supplemental material for both students and instructors. Data sets and R code (R
Language and Environment for Statistical Computing) are provided for
all but the introductory chapter and are integral to the text and the
exercises. Both students and instructors will welcome the 459-page set
of chapter-by-chapter lecture note slides in pdf. Instructors will find
all of the necessary material, including graphics and macros, to
typeset their own personalized version of the notes using LaTeX. In
less than 5 minutes, I was able to download and create dvi and pdf
files, complete with hyperlinks and without a hitch, using a standard
LaTeX installation from Fink on Darwin 8.9.1 (Mac OS X 10.4.9). The website also maintains the inevitable errata, and an exercise solution manual is available to instructors through the publisher.

I
was left wanting only a few things, which could be considered icing on
the cake. These include a list of distributions, perhaps with
annotation or with references to their use in the text, a list of symbols or functions used in the text, and perhaps a list of sampling algorithms.

Students
and instructors will undoubtedly find the book’s pace brisk but
refreshing, interesting, and fun. As an instructor of Bayesian
statistics courses, I was pleased to discover this ready- and
well-made, self-contained introductory course for (primarily) graduate
students in statistics and other quantitative disciplines I am seriously considering Bayesian Core for my next course in Bayesian statistics.

Jarrett J. BARBER

University of Wyoming