Bayesian Statistical Modelling. (Book Reviews)

Article excerpt

Peter CONGDON. Chichester, UK: Wiley, 2001. ISBN 0-471-49600-6. xi+531 pp. $65.00 (H).

Applied Bayesian statisticians, researchers in applications areas in which Bayesian statistical analysis is standard; and statistics teachers have eagerly awaited a book that can serve as an introduction to the philosophy and methods of Bayesian statistics, as a guide to real-data analysis with the popular Bayesian software package WinBUGS (Spiegelhalter, Thomas, and Best 2000), and as a showcase of application areas in which Bayesian statistics are used. This superbly referenced book makes a very useful contribution in the latter two regards, but could prove confusing to a student or novice attempting to learn Bayesian concepts and procedures.

The author is a Research Professor in Statistical Geography in the Department of Geography, Queen Mary, University of London. His own research interests in health services research, health outcomes models, and medical geography are reflected in the abundance of examples related to health and social science.

Chapter 2, "Standard Distributions: Updating, Inference, and Prediction," introduces Bayesian prior specification, estimation, prediction, and hypothesis testing in the context of simple models, beginning with a normal likelihood with population mean unknown and population variance assumed known. Illustrating each model with an example based on a small dataset, the chapter proceeds through normal models with both mean and variance parameters unknown; comparison of means in two or more normal populations; likelihoods; binomial, Poisson, and multinomial likelihoods for categorical data; and multivariate normal and multivariate [tau] likelihoods.

The subsequent chapters present more advanced topics in Bayesian statistical modeling, which enable realistic modeling in many application areas. These include hierarchical modeling, models for temporally and spatially correlated data, linear and generalized linear regression, and survival analysis.

Data and WinBUGS code for the worked examples are available via ftp from ftp://www.wileyco.uk/pub/books/congdon. Because the WinBUGS programs are not quoted in the book (except for occasional brief code fragments)m the reader must download them to fully understand the examples and learn WinBUGS programming methods.

The examples contain many useful coding tricks in WinBUGS, including multivariate normal likelihood with some missing data (Example 2.18), use of the equals function in computing intervals to which values of latent variables must be constrained (Example 7.26), use of the step function in computing the probability that a team would rank best or worst in a league (Example 5.10), and implementation of a Dirichlet process prior (Example 6.27).

The comprehensive 19-page reference list consists primarily of statistics books and journals (both applied and methodological), and also includes journals in applications areas from which worked examples are drawn (e.g., Cognitive Science, British Journal of Cancer, Virology, Health Economics, and Scientific American).

Unfortunately, due possibly to poor proofreading, the book contains so many confusing misstatements that its usefulness as an introductory text is very limited. The following are two representative examples. In Chapter 2, in which Congdon presents the basic Bayesian framework in the context of preparing for a Bayesian test of hypotheses, he states (p. 15):

The choice between which of two or more hypotheses to accept involves specifying prior beliefs about their relative frequency, and a comparison (after seeing the data) of their posterior probabilities. …