EM Algorithm and Extensions

Name: EM Algorithm and Extensions
Price: 86.97 USD
Availability: InStock
ISBN: 9780471201700

ISBN-10: 0471201707

ISBN-13: 9780471201700

Edition: 2nd 2008 (Revised)

Authors: Geoffrey J. McLachlan, Thriyambakam Krishnan

List price: $148.00

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This new edition remains the only single source to offer a complete and unified treatment of the theory, methodology, and applications of the EM algorithm. The highly applied area of statistics here outlined involves applications in regression, medical imaging, finite mixture analysis, robust statistical modeling, survival analysis, and repeated-measures designs, among other areas. The text includes newly added and updated results on convergence, and new discussion of categorical data, numerical differentiation, and variants of the EM algorithm. It also explores the relationship between the EM algorithm and the Gibbs sampler and Markov Chain Monte Carlo methods. With plentiful pedagogical…

Book details

List price: $148.00
Edition: 2nd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 3/14/2008
Binding: Hardcover
Pages: 400
Size: 6.00" wide x 9.50" long x 1.00" tall
Weight: 1.540
Language: English

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…



Preface to the Second Edition


Preface to the First Edition


List of Examples



General Introduction.



Introduction



Maximum Likelihood Estimation



Newton-Type Methods



Introductory Examples



Formulation of the EM Algorithm



EM Algorithm for MAP and MPL Estimation



Brief Summary of the Properties of EM Algorithm



History of the EM Algorithm



Overview of the Book



Notations



Examples of the EM Algorithm.



Introduction



Multivariate Data with Missing Values



Least Square with the Missing Data



Example 2.4: Multinomial with Complex Cell Structure



Example 2.5: Analysis of PET and SPECT Data



Example 2.6: Multivariate t-Distribution




Finite Normal Mixtures



Example 2.9: Grouped and Truncated Data



Example 2.10: A Hidden Markov AR(1) Model



Basic Theory of the EM Algorithm.



Introduction



Monotonicity of a Generalized EM Algorithm



Monotonicity of a Generalized EM Algorithm



Convergence of an EM Sequence to a Stationary Value



Convergence of an EM Sequence of Iterates



Examples of Nontypical Behavior of an EM (GEM) Sequence



Score Statistic



Missing Information



Rate of Convergence of the EM Algorithm



Standard Errors and Speeding up Convergence.



Introduction



Observed Information Matrix



Approximations to Observed Information Matrix: i.i.d. Case



Observed Information Matrix for Grouped Data



Supplemented EM Algorithm



Bookstrap Approach to Standard Error Approximation



Bakerï¿½s, Louisï¿½, and Oakesï¿½ Methods for Standard Error Computation



Acceleration of the EM Algorithm via Aitkenï¿½s Method



An Aitken Acceleration-Based Stopping Criterion



conjugate Gradient Acceleration of EM Algorithm



Hybrid Methods for Finding the MLE



A GEM Algorithm Based on One Newton-Raphson Algorithm



EM gradient Algorithm



A Quasi-Newton Acceleration of the EM Algorithm



Ikeda Acceleration



Extension of the EM Algorithm



Introduction



ECM Algorithm



Multicycle ECM Algorithm



Example 5.2: Normal Mixtures with Equal Correlations



Example 5.3: Mixture Models for Survival Data



Example 5.4: Contingency Tables with Incomplete Data



ECME Algorithm



Example 5.5: MLE of t-Distribution with the Unknown D.F



Example 5.6: Variance Components



Linear Mixed Models



Example 5.8: Factor Analysis



Efficient Data Augmentation



Alternating ECM Algorithm



Example 5.9: Mixtures of Factor Analyzers



Parameter-Expanded EM (PX-EM) Algorithm



EMS Algorithm



One-Step-Late Algorithm



Variance Estimation for Penalized EM and OSL Algorithms



Incremental EM



Linear Inverse problems



Monte Carlo Versions of the EM Algorithm.



Introduction



Monte Carlo Techniques



Monte Carlo EM



Data Augmentation



Bayesian EM



I.I.D. Monte Carlo Algorithm



Markov Chain Monte Carlo Algorithms



Gibbs Sampling



Examples of MCMC Algorithms



Relationship of EM to Gibbs Sampling



Data Augmentation and Gibbs Sampling



Empirical Bayes and EM



Multiple Imputation



Missing-Data Mechanism, Ignorability, and EM Algorithm



Some Generalization of the EM Algorithm.



Introduction



Estimating Equations and Estimating Functions



Quasi-Score and the Projection-Solution Algorithm



Expectation-Solution (ES) Algorithm



Other Generalization



Variational Bayesian EM Algorithm



MM Algorithm



Lower Bound Maximization



Interval EM Algorithm



Competing Methods and Some Comparisons with EM



The Delta Algorithm



Image Space Reconstruction Algorithm



Further Applications of the EM Algorithm.



Introduction



Hidden Markov Models



AIDS Epidemiology



Neural Networks



Data Mining



Bioinformatics


References


Author Index


Subject Index