Mixture models: inference and applications to clustering.

*(English)*Zbl 0697.62050
Statistics: Textbooks and Monographs, 84. New York etc.: Marcel Dekker, Inc. xi, 253 p. (1988).

The book gives a comprehensive account of the theoretical and computational issues for likelihood estimation in a finite mixture framework. Emphasizing the importance of mixture models in cluster analysis, the book shows how this approach to clustering provides a framework for assessing the number of clusters and their effectiveness. It also gives a detailed description of how bootstrap methodology can be used in these clustering problems. Numerous examples involving the statistical analyses of real data sets are presented throughout to demonstrate the various applications of finite mixture models. A FORTRAN listing of computer programs is given in the Appendix for the fitting of normal mixture models to data sets from a variety of experimental designs. It also contains a review of items concerned with the actual fitting of mixture models, such as detection of atypical observations, assessment of model fit, and robust estimation.

The contents are the following: 1. General introduction; 2. Mixture models with normal components; 3. Applications of mixture models to two- way data sets; 4. Estimation of mixing proportions; 5. Assessing the performance of the mixture likelihood approach to clustering; 6. Partitioning of treatment means in ANOVA; 7. Mixture likelihood approach to the clustering of three-way data. Over 350 references are given.

The book is an invaluable resource for applied and theoretical statisticians, biometricians, engineers in pattern recognition and psychologists.

The contents are the following: 1. General introduction; 2. Mixture models with normal components; 3. Applications of mixture models to two- way data sets; 4. Estimation of mixing proportions; 5. Assessing the performance of the mixture likelihood approach to clustering; 6. Partitioning of treatment means in ANOVA; 7. Mixture likelihood approach to the clustering of three-way data. Over 350 references are given.

The book is an invaluable resource for applied and theoretical statisticians, biometricians, engineers in pattern recognition and psychologists.

Reviewer: T.Postelnicu

##### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |