Applied Stochastic Modelling. (Book Reviews).

Applied Stochastic Modelling, by Byron J. T. MORGAN, New York: Oxford University Press, 2000, ISBN 0-340-74041-8, xxii+297 pp., $34.95 (paper).

There is almost universal agreement that statistics courses can be improved by more emphasis on real data analysis. Many recent introductory

statistics textbooks are taking this to heart, including in their pages more and more real world examples and case studies. However, for the instructor of a higher-level stats course who wants to make their course application-centered, there are still too few textbooks to choose from. This book is an attempt to remedy that problem.

This text is geared for a course in statistical modelling and/or data analysis for upper-level undergraduates and beginning graduate students. It is also intended as a reference for researchers using modem statistical methods. Its strength is unquestionably the varied and numerous examples taken from applications in mostly biology, but also psychology, geology, sociology, and economics. The book is heavily geared to using the computer for simulation and for data analysis, and over 50 Matlab programs are included throughout the book. S-Plus versions are available at the book's website at www.arnoldpublishers.com/support/stochastic.

The book begins by introducing 10 varied data sets and posing questions of statistical inference and modelling. A few of these examples are fertility cycles to conception for smokers and non-smokers; incubation periods for streptococcal sore throat gotten from drinking contaminated milk; mortality of flour beetles sprayed with insecticides; and incidence of diseased trees in a forest.

Chapter 2 presents basic material on model fitting using the method of maximum likelihood. Three examples are treated in depth, fitting a geometric, beta-geometric, and Poisson process model. The next chapter treats question of functional optimization in the context of maximizing the likelihood function. Both deterministic (Newton--Raphson, steepest descent, simplex search) and stochastic (simulated annealing) methods are presented, with many computer-based examples. Chapters 4 and 5 contain the bulk of the more theoretical material in the book, focusing on likelihood-based issues in statistical inference. Topics here include Fisher information, estimating errors and correlations, confidence regions, hypothesis testing, parametrization, and the EM algorithm. Chapter 6 is devoted to simulation techniques, including Monte Carlo and the bootstrap. Chapter 7 presents materials on Bayesian methods and Markov chain Monte Carlo. And the final chapter discusses general families of models, including generalized linea r, linear mixed, and additive models.

The text contains three appendices: (i) a basic probability and statistics reference section, with subsections on distributions, the Poisson process, normal quadratic forms, and Markov chains, (ii) Matlab primer, and (iii) material on kernel density estimation. There are numerous exercises, many involving some programming, at the end of each section. Solutions and comments are provided for selected problems.

The book is based on lecture notes given to a 30-hour lecture course for third-year undergraduates, statistics MSc students, and first-year statistics Ph.D. students at the University of Kent in England.

There is a wealth of material in this book, and even were it not adopted for a course, it could be an excellent reference. One hesitation in adopting this book for a course is that the theoretical material is somewhat thin. For use in a course, several sections might need supplementation. For instance, there is little motivation or development of the likelihood function. The book "hits the ground running" in its assumption that the reader is well versed on its use and applications. Also several examples are quite involved and could warrant more motivation and explanation. Nevertheless, I found the book very well written, fresh in it style, with lots of wonderful examples and problems. It is well referenced with almost 200 cited papers. An additional strength are the exercises at the end of each chapter, which are well thought out with a nice mix of routine questions, theoretical problems, programming assignments, and problems posed from current statistics papers. The solutions and comments section at the bac k of the book makes an attempt to lead students to the right answer by providing hints and suggestions on how to approach the problem, rather than just presenting the correct answer.

In the introduction the author writes that "[t]he construction, fitting and evaluation of statistical and stochastic models are not only vitally important... they are also great fun. It is hoped that some of the enjoyment and fascination of the subject will be gained by readers of this book." They were certainly gained by this reviewer.