% LaTeX source for review in Significance
\documentclass{article}
\newcommand{\hi}{\par\noindent\hangindent=1em}
\begin{document}
\hi
\textit{P M Lee, Bayesian Statistics: AN Introduction, Arnold, London
xv$+ 351$pp; 2004; \pounds19.99; ISBN 0 340 81405 5}
\smallskip
\hi
\textit{W M. Bolstad, Introduction to Bayesian Statistics, Wiley, New York,
xviii$+ 354$ pp; 2004, \pounds50.5050 50, ISBN 0 471 27020 2}
\bigskip
\noindent
As their titles suggest, both of these books aim to Provide an
introduction to Bayesian statistics---Lee's book was derived from his
notes used to teach a final year undergraduate class in the UK, whereas
Bolstad's aim was to teach this subject at the earliest possible stage
to undergraduates in New Zealand. So, although the books for the most
part cover the same topics, this difference in origins has ted to a
marked difference in presentation.
Lee is on his third edition, but the bulk of the first six chapters is
unchanged from the original.
These cover the usual introductory topics: probability, random
variables, inference for normal and other common distributions,
hypothesis tests, two-sample problems and simple general linear models.
Each topic is covered in a succinct manner, although this may not be
best suited to the majority who wish to use it for self-study. However,
exercises are provided at the end of each chapter with answers available
via the web.
Bolstad's book begins with three chapters that cover more fundamental
statistical and scientific data-gathering issues. He briefly discusses
some of the philosophical issues concerning the way knowledge is
obtained, going on to contrast the main approaches to
statistics---although the likelihoodists may claim they deserve some
mention here also. Different types of study and experimental designs are
also discussed, providing a basic introduction to this very important
subject. The last of these opening chapters covers the commonly used
ways of summarising and displaying data. Bolstad emphasises that ``Data
should always be looked at in several ways as the first stage in any
statistical analysis'', which, although it may be obvious to most, is
still too important a message not to be included in any introductory
statistics book (even for Bayesians!).
Chapters 4--13 of Bolstad essentially cover the same ground as chapters
1--6 in Lee. Whereas Lee appears to be coming to the subject from a
strong mathematical background, Bolstad is less mathematically
demanding. So in Lee you will read about minimal sufficiency and
data-translated likelihoods, whereas Bolstad builds up the concept of a
probability density function as the limiting form of a histogram. As
well as having exercises at the end of each chapter, with selected
answers at the back of the book, Bolstad also includes a bullet point
list of main points for each chapter. This is an excellent idea, not
only helping the learning process but also providing an additional means
to navigate the book. Another feature that gives this book a modern feel
is the inclusion of Monte Carlo exercises. These are based on Minitab
and R programs that can be obtained via the web.
The final three chapters of Lee cover more advanced topics that are not
in Bolstad at all. These include brief discussions of the likelihood
principle, stopping rules, Bayesian decision theory, hierarchical models
and numerical methods such as the Gibbs sampler. It is the addition of
these last two topics, given a chapter each, that makes up the main
changes since the previous edition. Clearly it is difficult to cover
too much in a single chapter on hierarchical models, and I am not sure
Lee has succeeded in whetting the reader's appetite for more. The final
chapter gives a reasonable explanation of the various numerical methods
currently used. I was pleased to see WinBUGS introduced, but
disappointed with the rather unorthodox example used to demonstrate its
application.
Perhaps in line with his more applied approach, Bolstad does include
some discussion of how meaningful prior information could be elicited.
Lee focuses on reference priors, with Bernardo's work in this area being
added to the latest edition. Bolstad also illustrates how to assess the
sensitivity of the inferences to the choice of prior. In fact, he goes
beyond this by including a final chapter on how to develop a model that
is robust to an incorrectly specified prior. This is done via a mixture
of conjugate priors, which is motivated and explained in a very
convincing manner. Although I was initially surprised to see this topic
covered in an introductory text, I believe it not only follows on nicely
from the earlier discussion of informative priors but also provides a
practical example of how the prior can justifiably be used to provide a
real advantage over the classical approach. In summary, Lee's book
provides a reasonable introduction to Bayesian statistics, which is
written very much in the style of a final year undergraduate text. I
believe Bolstad's book could be used to cover the same ground, albeit
with some of the more fundamental theoretical aspects missing. However,
Bolstad's is the book I would recommend to anyone wanting to self-study.
My only gripes with it are the paucity of references for the reader who
seeks more detail on a particular topic (only 15 references in the whole
book), the tack of critical discussion of the use of statistical
hypothesis tests (instead of simply providing a Bayesian version of
these) and the absence of a chapter introducing the need for Markov
chain Monte Carlo software including worked examples using a
free-to-user package such as WinBUGS.
I will keep both of these books on my shelf, but I expect that Bolstad
wilt be the one most borrowed by my colleagues.
\begin{flushleft}
\textit{Phil Woodward}
\smallskip
\textit{Herne}
\end{flushleft}
\begin{flushright}
From \textit{Significance} \textbf{1} (2004), 185.
\end{flushright}
\end{document}
%