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The EM Algorithm and Extensions, 2nd edition

Author: Geoffrey McLachlan

Publisher: Wiley


Publish Date: March 14, 2008

ISBN-10: 471201707

Pages: 400

File Type: PDF

Language: English

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Book Preface

The second edition attempts to capture significant developments in EM methodology in the ten years since the publication of the first edition. The basic EM algorithm has two main drawbacks-slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates. Moreover, some complex problems lead to intractable E-steps, for which Monte Carlo methods have been shown to provide efficient solutions. There are many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms, especially EM with data augmentation and Gibbs sampling. Furthermore, the key idea of the EM algorithm where a surrogate function of the log likelihood is maximized in a iterative procedure occurs in quite a few other optimization procedures as well, leading to a more general way of looking at EM as an optimization procedure.

Capturing the above developments in the second edition has led to updated, revised, and expanded versions of many sections of the first edition, and to the addition of two new chapters, one on Monte Carlo Versions of the EM Algorithm (Chapter 6) and another on Generalizations of the EM Algorithm (Chapter 7). These revisions and additions have necessitated the recasting of the first edition’s final (sixth) chapter, some sections of which have gone into the new chapters in different forms. The remaining sections with some additions form the last chapter with the modified title of “Further Applications of the EM Algorithm.”

The first edition of this book appeared twenty years after the publication of the seminal paper of Dempster, Laird, and Rubin (1977). This second edition appears just over ten years after the first edition. Meng (2007) in an article entitled “Thirty Years of EM and Much More” points out how EM and MCMC are intimately related, and that both have been “workhorses for statistical computing”. The chapter on Monte Carlo Versions of the EM Algorithm attempts to bring out this EM-MCMC connection

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