Finite Mixture Models (Wiley Series in Probability and Statistics) [Hardcover]

Geoffrey McLachlan (Author), David Peel (Author)

Book Description

ISBN-10: 0471006262 | ISBN-13: 978-0471006268 | Publication Date: October 2, 2000 | Edition: 1

An up-to-date, comprehensive account of major issues in finite mixture modeling
This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts.
Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide:
* Provides more than 800 references-40% published since 1995
* Includes an appendix listing available mixture software
* Links statistical literature with machine learning and pattern recognition literature
* Contains more than 100 helpful graphs, charts, and tables
Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

Editorial Reviews

Review

"This is an excellent book.... I enjoyed reading this book. I recommend it highly to both mathematical and applied statisticians." (Technometrics, February 2002)

"This book will become popular to many researchers...the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol. 963, 2001/13)

"the material covered is so wide that it will make this book a standard reference for the forthcoming years." (Zentralblatt MATH, Vol.963, No.13, 2001)

"This book is excellent reading...should also serve as an excellent handbook on mixture modelling..." (Mathematical Reviews, 2002b)

"...contains valuable information about mixtures for researchers..." (Journal of Mathematical Psychology, 2002)

"...a masterly overview of the area...It is difficult to ask for more and there is no doubt that McLachlan and Peel's book will be the standard reference on mixture models for many years to come." (Statistical Methods in Medical Research, Vol. 11, 2002)

"...they are to be congratulated on the extent of their achievement..." (The Statistician, Vol.51, No.3)

From the Back Cover

An up-to-date, comprehensive account of major issues in finite mixture modeling

This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts.

Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide:
* Provides more than 800 references-40% published since 1995
* Includes an appendix listing available mixture software
* Links statistical literature with machine learning and pattern recognition literature
* Contains more than 100 helpful graphs, charts, and tables

Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.

See all Editorial Reviews

Product Details

• Hardcover: 456 pages
• Publisher: Wiley-Interscience; 1 edition (October 2, 2000)
• Language: English
• ISBN-10: 0471006262
• ISBN-13: 978-0471006268
• Product Dimensions: 9.6 x 6.5 x 1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #416,183 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

33 of 34 people found the following review helpful:

5.0 out of 5 stars Job well done, April 26, 2001

By 

Random Thoughts (Maryland) - See all my reviews

Amazon Verified Purchase

This review is from: Finite Mixture Models (Wiley Series in Probability and Statistics) (Hardcover)

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...

23 of 23 people found the following review helpful:

5.0 out of 5 stars excellent coverage of mixture models and likelihood inference with EM algorithm applications, January 23, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Finite Mixture Models (Wiley Series in Probability and Statistics) (Hardcover)

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.

9 of 10 people found the following review helpful:

5.0 out of 5 stars Wonderful!, June 16, 2001

By A Customer

This review is from: Finite Mixture Models (Wiley Series in Probability and Statistics) (Hardcover)

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.