Joseph Hilbe

English

Research Papers in Economics

JSS Journal of Statistical Software
July 2007, Volume 21, Book Review 1. http://www.jstatsoft.org/
Reviewer: Joseph Hilbe
Arizona State University
Bayesian Core: A Practical Approach to Bayesian Computational Statistics
Jean-Michel Marin and Christian P. Robert
Springer-Verlag, New York, NY, 2007.
ISBN 978-0-387-38979-0. 255 pp. USD 74.95 (P).
http://www.ceremade.dauphine.fr/~xian/BCS/
The authors, Marin from Universit´ e Paris-Sud, and Robert, from Universit´ e Paris-Dauphine,
have attempted to produce an intermediate level text on Bayesian statistics aimed for use by
graduate students who need to have a fundamental understanding of Bayesian methods for
their research. The authors also intend the book to be useful to scientists in all disciplines
who may need to use Bayesian statistics. For several years both authors have taught a
course corresponding to the text as part of a second year masters program for students in
data processing as well as in statistics. The aim is to have readers learn to think about the
purpose of a Bayesian analysis and to develop an intuition of what their analytic results should
look like. Exercises are found throughout the text, rather than at the end of each chapter.
The hope is to have readers get a more immediate feedback about what they are learning as
they progress through the material. This way, inaccuracies in thinking can be caught early in
the learning process. My impression of the text is that it is more of a handbook on Bayesian
methods than a traditional textbook. The writing style is generally clear and to the point.
The subject matter is for the most part developed in a step by step manner, with an eﬀort
taken to clarify major concepts and equations as they develop in the discussion. The authors
have chosen to employ R for all examples, and even have a section in the text entitled, “A
short introduction to R.” However, the use of examples showing R code in the text is for the
most part dropped after Chapter 4.
Chapter 1: User’s manual
In their opening chapter the authors provide guidelines regarding prerequisites, styles and
fonts used in the text, and an overview of R programming. This section provides a summary
of relevant R objects, a listing of probability distributions in R, a guide on how to write R
functions, a discussion of how to read ﬁles into an R function and how to display results, and
the administration of R objects. The section, “A short introduction to R,” is helpful to those
having no background in R programming, and it indeed corresponds to the section title – “A2 Bayesian Core: A Practical Approach to Bayesian Computational Statistics
short sntroduction.” One can in no way read the section and begin useful R programming.
However, it is a good base from which a course instructor can enlarge on the subject.
Chapter 2: Normal models
The chapter begins with a brief overview of the normal or Gaussian model. The authors
commence by developing a normally distributed histogram of temperature diﬀerences inherent
in the cosmic microwave background (CMB) radiation reﬂecting the universe as it was when
the cosmic temperature was cool enough to allow the formaton of atoms. The next section is
titled,“The Bayesian toolkit.” It is here where the authors bring up the notions of information,
priors, and posteriors. Readers are also introduced to the exponential family of distributions,
which underlay generalized linear models. Following this discussion, the subjects of conﬁdence
intervals and then hypothesis testing are addressed. The ﬁrst chapter ends with a section on
Monte Carlo methods and importance sampling. The discussion in the second chapter is not
as elementary as the authors would have readers believe in the introduction. It starts out in
an rather easy manner, but quickly diverges into more diﬃcult methods, giving the reader a
minimum of supporting background. It is likely that many masters level students will need
additonal instructor support, even at this early point in the text.
Chapter 3: Regression and variable selection
This is one of the better chapters in the text. After presenting a clearly written overview
of the traditional approach to OLS regression, the authors address the Bayesian approach to
the Gaussian model. They ﬁrst discusses the notion of conjugate priors, which is basic to
Bayesian thinking. Zellner’s G-prior, Jeﬀrey’s prior, and Zellner’s non-informative G-prior
are discussed in detail. The next section in the chapter deals with Markov chain Monte Carlo
(MCMC) methods and an overvidew of how a two-stage Gibb sampler works. Generic R code
is given to allow readers use of Gibbs sampling with their own data. Finally, the authors
describe Bayesian methods of variable selection in modeling building. An interesting data
set, called catepillar, is used for examples.
Chapter 4: Generalized linear models
The authors focus on binary response logit and probit models as well as log-linear or Poisson
count response model to demonstrate Bayesian modeling from within the generalized linear
model (GLM) framework. Of course, the Gaussian model examined in the previous chapter
is also a GLM, but typically Gaussian or normal linear modeling is considered separately, as
it is in this text. The authors begin the chapter by providing an overview of the Metropolis-
Hastings algorithm (M-H) which is used for the simulation of more complex distributions
when both standard and Gibbs sampling fail to work. As a Markov chain Monte Carlo type
algorithm, the M-H algorithm includes a random walk component. The algorithm has an
essential role in the modeling of Bayesian GLMs. A data set containing information on both
genuine and counterfeit bank notes is used for the majority of this chapter. The authors
do a good job explaining the basics of GLM, including a thorough section on link functions.
They detail the M-H algorithm, showing a step-by-step outline of the algorithm. Separate
sections are then given to the modeling of the bank note data using Bayesian probit and thenJournal of Statistical Software – Book Reviews 3
logit models. The Poisson model uses a separate data set, called airquality. For each section,
the authors give R code on inputting and formatting the data, and subsequently modeling
it. Both traditional GLM methods, usually built on a variety of iteratively re-weighted least
squares algorithm, and the M-H method of parameter estimation for Bayesian-based models
are shown.
Chapter 5: Capture-recapture experiments
This chapter deals with a special case of survey models. Emphasis is given to capture-
recapture surveys, where persons are observed repeatedly over time. The repeated obser-
vations can then be used to draw inferences regarding the population size and the inherent
dynamic properties of the population as a whole. Various sampling models are discussed,
including the binomial capture model, the two-stage capture-recapture model, the T-stage
capture-recapture model, the open population model, and the Arnason-Schwarz capture-
recapture model. The accept-reject sampler algorithm is demonstrated using several clearly
written examples.
Chapter 6: Mixture models
This chapter and the following two are technically more diﬃcult than the preceding chapters.
Chapter 5 is of intermediate complexity. The authors use the same style of writing in these
chapters, but the subject material itself is more complex. Essentially, this chapter is devoted to
an examination of several mixture models and their MCMC solution. The most extensively
discussed mixture is the normal-normal, which is clearly described. Mean mixture Gibbs
sampler and mean mixture M-H sampler algorithms are described in detail and illustrated
with example output, including graphical displays. Other more complex algorithms are then
discussed. Each is a type of MCMC-based algorithm. Included in this group are variable
dimension models and reversible jump MCMC models.
Chapter 7: Dynamic models
The authors warn readers that this chapter contains more advanced material. And so it does.
The primary focus of the chapter is to show the Bayesian processing of standard time-series
models including the autoregressive, moving average, and ARIMA models. Moreover, the
authors also discuss models whose dependence is evaluated by means of a missing variable
structure. Such models belong to a variety of hidden Markov model that was ﬁrst discussed
in the previous chapter. Stochastic volatility ﬁnance models are included in this class. In
the earlier parts of the chapter, the authors emphasize basic temporal or dynamic models,
indexed only by time. These models use a Markov dependence structure, which was discussed
in Chapters 5 and 6. One of the better algorithms presented in the text is the reversible
jump AR(p) sampler used for autoregressive models. Although discussed brieﬂy in previous
sections, a thorough section on hidden Markov models is presented at the end of the chapter.
Chapter 8: Image analysis
Image analysis has been a major application of Bayesian methods for the past quarter century.4 Bayesian Core: A Practical Approach to Bayesian Computational Statistics
The authors bring two approaches to bear on the topic. First they discuss classiﬁcation anal-
ysis – in particular, k-nearest neighbor methods. Secondly, they focus on pattern recognition
and image correction, based on Potts modeling, and in the case of binary images, Ising models.
Included in the discussion are the more advanced topics of Markov random ﬁelds and general
spatial analysis. The Metropolis-Hastings sampler algorithm is used for simulation modeling
of image and spatial data. A specialized application of the M-H algorithm for image data is
shown in detail in the text. This is a most useful guide for those who need to implement these
methods into their research. Astrostatistics and Geostatistics are two major applied areas of
statistics that heavily use image analysis in research. It is an advanced statistical method,
but the authors do a fairly good job in making it as clear as possible.
Concluding remarks
The text is an intermediate-advanced overview of Bayesian methods and how they can be
applied to certain areas of research. In the preface the authors would have prospective readers
think that the text is a bit more more elementary than it is. When viewed in comparison to a
text like Gill (2002), it is evident that Bayesian Core is written at a higher level of complexity.
However, for graduate students relying on Bayesian methods for the research on areas related
to speciﬁc topics discussed in the text, the book could prove to be an invaluable guide.
The authors do not provide the Web address where readers can download the data sets
and R code used for examples. However, they do mention in several places that all data
sets and code can be found on the authors’ Web site. The address is also provided on
Springer’s Web page for the book. In fact, the Springer page allows one to directly click on
the authors’ homepage URL. Data sets and all R code are found at this latter site, which is
http://www.ceremade.dauphine.fr/~xian/BCS/. A solution manual is also available from
Springer, with instructions and an application form for use given on the Springer site. See
http://www.springer.com/west/home?SGWID=4-102-22-173676531-0.
I would have preferred that the author’s URL would have been listed in the text, as well as
the URL for the Springer page for the book. I nevertheless recommend the book for classroom
use in advanced masters and Ph.D. level courses in Bayesian methodology. The book can be
used in undergraduate settings, but only with substantial support from the instructor.
References
Gill J (2002). Bayesian Methods: A Social and Behavioral Sciences Approach. Chapman &
Hall/CRC, Boca Raton, Florida, 2nd edition.Journal of Statistical Software – Book Reviews 5
Reviewer:
Joseph Hilbe
Arizona State University
School of Social and Family Dynamics
Tempe, AZ, United States of America
E-mail: hilbe@asu.edu
URL: http://en.wikipedia.org/wiki/Joseph_Hilbe
Journal of Statistical Software http://www.jstatsoft.org/
published by the American Statistical Association http://www.amstat.org/
Volume 21, Book Review 1 Published: 2007-07-30
July 2007

Bayesian Core: A Practical Approach to Bayesian Computational Statistics

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