Customer Reviews

Finite Mixture Models (Wiley Series in Probability and Statistics)

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Mixture models have become a hot topic in statistics. After you read this book, you will know why.

"Finite Mixture models" have come a long way from classic finite mixture distribution as discused e.g. Titterington et al(1985). A small sample should almost surely entice your taste, with hot items such as hierarchical mixtures-of-experts models, mixtures of GLMs, mixture models for failure-time data, EM algorithms for large data sets, and hidden Markov models. The book gives a lucid overview of recent developments on mixture models since 1990 (the aim of this book in the first place). It expounds on the modern viewpoint that mixtures can be usefully exploited as a mechanism for building flexible statistical models for complex processes, e.g. nonparametric Bayesian models. Balanced attention is given to all three modern approaches to fitting mixture models which include speed-up EM, Bayesian, and stochastic simulation. The whole book is superbly written, and very entertaining---It's hard to put it down once started. It is very update with 45 pages of references and an appendix listing available softwares.

I'm a big fan of Prof. McLachlan's books; and I believe, this latest book of his with one of his student D. Peel, should add another masterpeiece to the long list of marvelous statistics books coming out of Australia and New Zealand...

McLachlan and Basford (1988) and Titterington, Smith and Makov (1985) were the first well written texts summarizing the diverse lterature and mathematical problems that can be treated through mixture models. Geoff McLachlan is the author of four statistics texts namely (1)McLachlan and Basford (1988) "Mixture Models:Inference and Applications to Clustering", Marcel Dekker, (2) McLachlan (1992) "Discriminant Analysis and Statistical Pattern Recognition", Wiley (3) McLachlan and Krishnan (1997) "The EM Algorithm and Extensions" Wiley and (4) McLachlan and Peel (2000) "Finite Mixture Models" Wiley. These four books are all related to the interesting problems in pattern recognition and clustering. Mixture models and the EM algorithm are tools used to solve problems in clustering and pattern recognition.

In each of his books McLachlan has shown an ability to be clear, authoritative, scholarly and thorough. He provides broad coverage of each topic with detailed references. This book is no exception. As he point out in the preface, the literature on mixture models has expanded tremendously since the appearance of his 1988 monograph with Kaye Basford making an updated text very appropriate.

Almost 40% of the 800 references in the text have appeared since 1995. The recent advances covered in the text include identifiability problems with mixture models, the analysis (fitting of mixture models) for real data sets using the EM algorithm and its extensions, properties of maximum likelihood estimators, applicability of asymptotic theory, use of bootstrap methods to assess accuracy of estimates, implimentation of Bayesian approaches through Markov chain Monte Carlo methods and the use of hierarchical mixtures-of-expert models for nonlinear regression as competitors to the MARS and CART algorithms.

This is a great book. Chapter 1 provides a nice overview of the subject with a thorough historical treatment, nicely presented in Section 1.18. In addition to the fact that it covers all the recent advances one can think of. The book also deals with fast implementations of the EM algorithm for data mining and other approaches to modifying the EM algorithm to handle large data sets. There is also a wealth of interesting real problems worked out in detail. These problems come from many disciplines, including interesting medical problems related to diabetes and hemophilia, nuclear test ban data analysis, image processing and competing risk survival analysis. It also covers some interesting aspects of multivariate normal mixture models and their applications.

A wonderful text that functions as well as a reference as it does as an introduction to mixture models. I was surprised by the depth and breadth of the book, which manages to describe almost every mixture model imaginable and then some more, including forms of the models themselves, parameter estimation and fit. Relationships between different models are made clear, lending the text a coherence that isn't undercut by vague generalities. The authors are particularly good at addressing issues of particular importance in mixture modeling, such as fit and model selection. Material is suprisingly recent as well. Overall, a great text that is probably destined to become the standard reference on mixture models.

This title is not up to the high standards set by McLachlan's other books. The text does not get into details which are thoroughly discussed
in McLachlan's excellent "The EM Algorithm and Extensions." Some important points are so condensed and in places so poorly presented that the the discussion is worthless. For example the important section 3.4 "Standard Errors", which underlies much of the discussion contains errors.
The book could be useful to a practioner who is only looking for guidance in fitting mixture models with available software. Unfortanately McLachlan's mixture software referred to in the Appendix, is not available. That's a pity because the advertised software features and design potentially rank it the top choice.
For a user who will use his own EM software to fit mixture models I would recommend highly the McLachlan's EM Algorithm book over the Mixture book.

"Finite Mixture Models" is an excellent reading for scientists and researchers working on or interested in finite mixture models. It provides a comprehensive introduction to finite mixture models as well as an extensive survey of the novel finite mixture models presented in the most recent literature on the field in conjunction with the prospective practical applications of them. In addition, the book is very well-written and it has the merit of the use of a consistent mathematical notation throughout the book.