REVIEW

\underline{THE EM ALGORITHM AND EXTENSIONS}. G.J. McLachlan and T. Krishnan. New York: Wiley, 1997, pp. xvii + 274, £50.00.

Contents:

1. General introduction

2. Examples of the EM algorithm

3. Basic theory of the EM algorithm

4. Standard errors and speeding up convergence

5. Extensions of the EM algorithm

6. Miscellaneous topics

Readership: Statisticians, undergraduate and graduate students

The EM algorithm has been around for a long time and is routinely used in incomplete data situations-where there are missing, censored or grouped data, or where truncated distributions are involved. It can also be used in some complete data situations for which maximum likelihood estimation has been found intractable, by reformulating the problem as an incomplete data problem. It is surprising therefore that a text such as this has not appeared earlier. Evidently it is the first one that focuses on the algorithm and gives a comprehensive treatment of the subject. Those wishing to understand the subject from scratch should find the early chapters give a very good introduction albeit with some effort on the part of the reader. There are plenty of good motivating examples drawn from the wide applicability of the method. The important issues of convergence and convergence rates are well covered and the recent evolution of the method to handle problems outside the scope of the conventional EM algorithm is discussed in some detail. Although not set up as a teaching text with exercises at the end of each chapter etc., the book should help promote the teaching of this important subject in postgraduate and appropriate undergraduate courses.

Macquarie University Sydney, Australia J.R. Leslie