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.
Extracts from Published Reviews:
(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.''
(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!''
``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.''
(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.
(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.''
``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.''
(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
(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.''
(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.''