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.

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