The Em Algorithm and Related Statistical

Exploring the application and formulation of the EM algorithm, The EM Algorithm and Related Statistical Models offers a valuable method for constructing statistical models when only incomplete information is available, and proposes specific estimation algorithms for solutions to incomplete data problems. The text covers current topics including statistical models with latent variables, as well as neural network models, and Markov Chain Monte Carlo methods. It describes software resources valuable for the processing of the EM algorithm with incomplete data and for general analysis of latent structure models of categorical data, and studies accelerated versions of the EM algorithm.

Preface

iii

Contributors

ix

1. Incomplete Data and the Generation Mechanisms

1

(8)

Michiko Watanabe

1. Incomplete Data Problems

1

(2)

2. Generation Mechanisms by Which Missing Data Arise

3

(5)

References

8

(1)

2. Incomplete Data and the EM Algorithm

9

(12)

Michiko Watanabe and Kazunori Yamaguchi

1. Analysis of Multivariate Data with Missing Values

9

(1)

2. Estimation of Missing Values

10

(5)

3. Maximum Likelihood Estimation Based on Incomplete Data

15

(2)

Summary

17

(1)

References

18

(3)

3. Statistical Models and the EM Algorithm

21

(16)

Kazunori Yamaguchi and Michiko Watanabe

1. Introduction

21

(3)

2. EM Algorithm

24

(3)

3. Properties of the EM Algorithm

27

(1)

4. Asymptotic Covariance Matrix via the EM Algorithm

28

(1)

5. Incomplete Data and the EM Algorithm

29

(2)

6. Examples

31

(3)

References

34

(3)

4. Robust Model and the EM Algorithm

37

(28)

Kazunori Yamaguchi

1. Linear Model with Heavy-Tailed Error Distributions

37

(12)

2. Estimation from Data with Missing Values

49

(2)

3. Robust Estimation in Factor Analysis

51

(9)

4. Robust Tobit Model

60

(2)

References

62

(3)

5. Latent Structure Model and the EM Algorithm

65

(6)

Michiko Watanabe

1. Introduction

65

(1)

2. Latent Structure Model

66

(2)

3. The EM Algorithm for Parameter Estimation

68

(2)

References

70

(1)

6. Extensions of the EM Algorithm

71

(14)

Zhi Geng

1. Partial Imputation EM Algorithm

71

(3)

2. Convergence of the PIEM Algorithm

74

(6)

3. Examples

80

(3)

References

83

(2)

7. Convergence Speed and Acceleration of the EM Algorithm

85

(10)

Mihoko Minami

1. Introduction

85

(1)

2. Convergence Speed

85

(3)

3. Comparison of Computing Time

88

(3)

4. Acceleration Methods

91

(2)

References

93

(2)

8. EM Algorithm in Neural Network Learning

95

(32)

Noboru Murata and Shiro Ikeda

1. Introduction

95

(1)

2. EM Algorithm and EM Algorithm

96

(11)

3. EM Algorithm as Learning Rules

107

(12)

4. Module Models for EM Algorithm

119

(5)

References

124

(3)

9. Markov Chain Monte Carlo

127

(32)

Masahiro Kuroda

1. Introduction

127

(1)

2. Markov Chains

128

(2)

3. The Data Augmentation Algorithm

130

(7)

4. The Gibbs Sampling Algorithm

137

(10)

5. The Metropolis-Hastings Algorithm

147

(8)

Bibliographic Notes

155

(1)

References

156

(3)

Appendix A. SOLAS™ 3.0 for Missing Data Analysis

159

(30)

Appendix B. l EM

189

(6)

Index

195

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The Em Algorithm and Related Statistical Models

Summary

Table of Contents

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