# The EM Algorithm and Extensions (Wiley Series in Probability and Statistics)

## Geoffrey McLachlan; Thriyambakam Krishnan

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The first unified account of the theory, methodology, and applications of the EM algorithm and its extensions

Since its inception in 1977, the Expectation-Maximization (EM) algorithm has been the subject of intense scrutiny, dozens of applications, numerous extensions, and thousands of publications. The algorithm and its extensions are now standard tools applied to incomplete data problems in virtually every field in which statistical methods are used. Until now, however, no single source offered a complete and unified treatment of the subject.

The EM Algorithm and Extensions describes the formulation of the EM algorithm, details its methodology, discusses its implementation, and illustrates applications in many statistical contexts. Employing numerous examples, Geoffrey McLachlan and Thriyambakam Krishnan examine applications both in evidently incomplete data situations—where data are missing, distributions are truncated, or observations are censored or grouped—and in a broad variety of situations in which incompleteness is neither natural nor evident. They point out the algorithm's shortcomings and explain how these are addressed in the various extensions.

Areas of application discussed include:

• Regression
• Medical imaging
• Categorical data analysis
• Finite mixture analysis
• Factor analysis
• Robust statistical modeling
• Variance-components estimation
• Survival analysis
• Repeated-measures designs

For theoreticians, practitioners, and graduate students in statistics as well as researchers in the social and physical sciences, The EM Algorithm and Extensions opens the door to the tremendous potential of this remarkably versatile statistical tool.

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A unified and complete treatment of the theory and methodology of the Expectation-Maximization (EM) algorithm, its extensions and their applications. Applications in standard statistical contexts such as regression, factor analysis, variance-components estimation, repeated-measures designs, categorical data analysis, survival evaluatio, and survey sampling are covered, as well as applications in other areas like genetics and psychometry. Approximately 30 examples illustrate the theory and methodology.

Geoffrey J. McLachlan, PhD, DSc, is Professor of Statistics in the Department of Mathematics at The University of Queensland, Australia. A Fellow of the American Statistical Association and the Australian Mathematical Society, he has published extensively on his research interests, which include cluster and discriminant analyses, image analysis, machine learning, neural networks, and pattern recognition. Dr. McLachlan is the author or coauthor of Analyzing Microarray Gene Expression Data, Finite Mixture Models, and Discriminant Analysis and Statistical Pattern Recognition, all published by Wiley.

Thriyambakam Krishnan, PhD, is Chief Statistical Architect, SYSTAT Software at Cranes Software International Limited in Bangalore, India. Dr. Krishnan has over forty-five years of research, teaching, consulting, and software development experience at the Indian Statistical Institute (ISI). His research interests include biostatistics, image analysis, pattern recognition, psychometry, and the EM algorithm.

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## 1.The EM Algorithm and Extensions (Wiley Series in Probability and Statistics)

Verlag: Wiley-Interscience (1996)
ISBN 10: 0471123587 ISBN 13: 9780471123583
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Buchbeschreibung Wiley-Interscience, 1996. Hardcover. Buchzustand: Sehr gut. 1. Auflage. Sehr guter Zustand. A-383. Artikel-Nr. 5-OKT-00201

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