The EM Algorithm and Extensions
    (Wiley series in Probability and Mathematical Statistics: Applied Probability and Statistics Section) by G.J. McLachlan and T. Krishnan. New York; John Wiley & Sons, Inc. 1997, xvii + 274 pp.
    ISBN 0-471-12358-7.
    Extracts from Published Reviews:
    Ambroise (1998, Journal of Classification) ``Some excellent books have already appeared, which are partly concerned with the EM algorithm (e.g., Little and Rubin 1987), but no book has been fully dedicated to the subject. The book by G.J. McLachlan and T. Krishnan fills this gap. It is organized in six chapters. Many examples from very different statistical areas are provided, and used for illustrating details of implementation, extensions of the algorithms or theory. They help the reader throughout the book. ... In conclusion, this is a good book, which is very pleasant to read. It contains a great variety of examples.''
    Diebolt (1998, Mathematical Reviews) ``The authors point out that despite the obvious importance (more than 1700 publications related to EM in 1996!) of the EM technique and its ramifications, no full-fledged book on the subject has so far appeared. Their purpose in writing this book was to fulfill the need for a unified and complete treatment of the EM algorithm and its extensions, and their applications. This book is aimed both at theoreticians and at practitioners of statistics. It is as self-contained as possible, and the main parts of the book should be comprehensible to graduates with statistics as their major subject. There is no doubt that the authors have reached their goal!''
    Gentle (1998, Biometrics) ``The EM algorithm has become one of the most widely-used statistical tools, ... There are many texts and articles that discuss various aspects of the EM algorithm, but this is the only book to give a unified view, covering the basic methodology and the underlying theory. Although there is a sequential development, building ever more complexity into the algorithm, the numerous examples keep the discussion accessible, and provide interesting casual reading. ... The bibliography is extensive, serving both for attribution of contributions to the subject and for further reading.''
    Heitjan (1998, Statistics in Medicine) The authors provide excellent syntheses of EM's theoretical underpinnings, the theory of its convergence, and the various ways in which it has been extended and refined. ... EM has become a core topic in the literature of incomplete data and statistical computing, and McLachlan and Krishnan have given us a thorough and readable account of its workings and history. Students and researchers who wish to learn about EM should look here first.
    Kahn (1998, The American Mathematical Monthly) ``Excellent resource for theory and application of EM algorithm and its many variations. Applications range from simple, one-parameter multinomials, to hidden Markov models, epidemiological models, and neural networks.''
    Kushary (1998, Technometrics) ``This is one of the first books on this subject, and the authors have done an excellent job organizing and presenting the materials and providing an up-to-date bibliography of the research papers. The monograph is organized in a suitable manner so that it is accessible and useful to statisticians interested in applications research. The writting style is clear and easy to understand. It should be comprehensible to graduates with statistics as their major subject. Throughout the book, the theory and methodology are illustrated with several examples, and analytical examples are followed up with numerical computations wherever relevant.''
    Leslie (1998, Short Book Reviews) ``There are plenty of good motivating examples drawn from a broad spectrum of contexts -- these serve to reinforce 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.''
    McCulloch (1998, Journal of the American Statistical Association) ``In my opinion the book's strongest contribution is in relating the various modifications and improvements of EM and in indicating relationships to alternate techniques. These are especially hard to establish on one's own, because it would require gathering together research in different journals, by different authors, in different notations. ... The references are quite up to date.''
    Prasaka Rao (1988, Zentralblatt fur Mathematik ``The authors have illustrated the theory with a large number of examples and the book is well-written. The material is presented at a level accessible to graduate students in statistics. I strongly recommend this book for all those interested in Statistical Inference and Data Analysis. It is a welcome addition to the literature on Statistical Inference.''
    References
  • Ambroise, C. (1998). Journal of Classification 15, 154-156.
  • Diebolt, J. (1998). Mathematical Reviews 98f (# 62057).
  • Gentle, J.E. (1998). Biometrics 54, 395-396.
  • Heitijan, D.F. (1998). Statistics in Medicine 17, 1187.
  • Kahn, M. (1998). The American Mathematical Monthly. Reprinted in Institute of the Mathematical Statistics Bulletin 27 , 24.
  • Kushary, D. (1998). Technometrics 40, 260.
  • Leslie, J.R. (1998). Short Book Reviews 18 (April Issue).
  • McCulloch, C.E. (1998). Journal of the American Statistical Association 93, 403-404.
  • Prasaka Rao, B.L.S. (1998). Zentralblatt fur Mathematik und ihre Grenzgebiete # 882.62012