The EM Algorithm and Extensions

The EM Algorithm and Extensions 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.

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.

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
BakerÆs, LouisÆ, and OakesÆ Methods for Standard Error Computation
Acceleration of the EM Algorithm via AitkenÆs 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
Table of Contents provided by Publisher. All Rights Reserved.

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