Bayesian missing data problems: EM, data augmentation and noniterative computation
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
Chapman & Hall
2010
|
| Series: | Chapman & Hall/CRC biostatistics series
32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 328 S. Ill. |
| ISBN: | 9781420077490 |
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MARC
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| 245 | 1 | 0 | |a Bayesian missing data problems |b EM, data augmentation and noniterative computation |c Ming T. Tan ; Guo-Liang Tian ; Kai Wang Ng |
| 264 | 1 | |a Boca Raton |b Chapman & Hall |c 2010 | |
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| 490 | 1 | |a Chapman & Hall/CRC biostatistics series |v 32 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Missing observations (Statistics) | |
| 700 | 1 | |a Tian, Guo-Liang |e Verfasser |4 aut | |
| 700 | 1 | |a Ng, Kai Wang |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | Titel: Bayesian missing data problems
Autor: Tan, Ming T.
Jahr: 2010
Contents
Preface xv
1 Introduction 1
1.1 Background........................ 1
1.2 Scope, Aim and Outline................. 6
1.3 Inverse Bayes Formulae (IBF).............. 9
1.3.1 The point-wise, function-wise and sampling IBF 10
1.3.2 Monte Carlo versions of the IBF........ 12
1.3.3 Generalization to the case of three vectors ... 14
1.4 The Bayesian Methodology............... 15
1.4.1 The posterior distribution............ 15
1.4.2 Nuisance parameters............... 17
1.4.3 Posterior predictive distribution ........ 18
1.4.4 Bayes factor.................... 20
1.4.5 Marginal likelihood................ 21
1.5 The Missing Data Problems............... 22
1.5.1 Missing data mechanism............. 23
1.5.2 Data augmentation (DA) ............ 23
1.5.3 The original DA algorithm ........... 24
1.5.4 Connection with the Gibbs sampler ...... 26
1.5.5 Connection with the IBF ............ 28
1.6 Entropy.......................... 29
1.6.1 Shannon entropy................. 29
1.6.2 Kullback-Leibler divergence........... 30
Problems ......................... 31
2 Optimization, Monte Carlo Simulation and
Numerical Integration 35
2.1 Optimization....................... 36
2.1.1 The Newton-Raphson (NR) algorithm..... 36
2.1.2 The expectation-maximization (EM) algorithm 40
2.1.3 The ECM algorithm............... 47
2.1.4 Minorization-maximization (MM) algorithms . 49
2.2 Monte Carlo Simulation................. 56
CONTENTS
2.2.1 The inversion method.............. 56
2.2.2 The rejection method .............. 58
2.2.3 The sampling/importance resampling method . 62
2.2.4 The stochastic representation method..... 66
2.2.5 The conditional sampling method........ 70
2.2.6 The vertical density representation method . . 72
2.3 Numerical Integration.................. 75
2.3.1 Laplace approximations............. 75
2.3.2 Riemannian simulation.............. 77
2.3.3 The importance sampling method ....... 80
2.3.4 The cross-entropy method............ 84
Problems ......................... 89
Exact Solutions 93
3.1 Sample Surveys with Nonresponse...........93
3.2 Misclassified Multinomial Model ............95
3.3 Genetic Linkage Model..................97
3.4 Weibull Process with Missing Data...........99
3.5 Prediction Problem with Missing Data.........101
3.6 Binormal Model with Missing Data...........103
3.7 The 2x2 Crossover Trial with Missing Data.....105
3.8 Hierarchical Models ...................108
3.9 Nonproduct Measurable Space (NPMS) ........109
Problems .........................112
Discrete Missing Data Problems 117
4.1 The Exact IBF Sampling ................118
4.2 Genetic Linkage Model..................119
4.3 Contingency Tables with One Supplemental Margin . 121
4.4 Contingency Tables with Two Supplemental Margins . 123
4.4.1 Neurological complication data.........123
4.4.2 MLEs via the EM algorithm ..........123
4.4.3 Generation of i.i.d. posterior samples......125
4.5 The Hidden Sensitivity (HS) Model for Surveys with
Two Sensitive Questions.................126
4.5.1 Randomized response models..........126
4.5.2 Nonrandomized response models........127
4.5.3 The nonrandomized hidden sensitivity model . 128
4.6 Zero-Inflated Poisson Model...............132
4.7 Changepoint Problems..................133
4.7.1 Bayesian formulation...............134
4.7.2 Binomial changepoint models..........137
CONTENTS xi
4.7.3 Poisson changepoint models...........139
4.8 Capture-Recapture Model................145
Problems.........................148
5 Computing Posteriors in the EM-Type Structures 155
5.1 The IBF Method.....................156
5.1.1 The IBF sampling in the EM structure .... 156
5.1.2 The IBF sampling in the ECM structure .... 163
5.1.3 The IBF sampling in the MCEM structure . . 164
5.2 Incomplete Pro-Post Test Problems...........165
5.2.1 Motivating example: Sickle cell disease study . 166
5.2.2 Binormal model with missing data and known
variance......................167
5.2.3 Binormal model with missing data and
unknown mean and variance ..........168
5.3 Right Censored Regression Model............173
5.4 Linear Mixed Models for Longitudinal Data......176
5.5 Probit Regression Models for Independent
Binary Data........................181
5.6 A Probit-Normal GLMM for Repeated Binary Data . 185
5.6.1 Model formulation................186
5.6.2 An MCEM algorithm without using
the Gibbs sampler at E-step...........187
5.7 Hierarchical Models for Correlated Binary Data . . . .195
5.8 Hybrid Algorithms: Combining the IBF Sampler
with the Gibbs Sampler.................197
5.8.1 Nonlinear regression models...........198
5.8.2 Binary regression models with t link......199
5.9 Assessing Convergence of MCMC Methods ......201
5.9.1 Gelman and Rubin s PSR statistic.......202
5.9.2 The difference and ratio criteria.........203
5.9.3 The Kullback-Leibler divergence criterion . . . 204
5.10 Remarks..........................204
Problems .........................206
6 Constrained Parameter Problems 211
6.1 Linear Inequality Constraints..............211
6.1.1 Motivating examples...............211
6.1.2 Linear transformation..............212
6.2 Constrained Normal Models...............214
6.2.1 Estimation when variances are known.....214
6.2.2 Estimation when variances are unknown .... 219
xii CONTENTS
6.2.3 Two examples ..................222
6.2.4 Discussion.....................227
6.3 Constrained Poisson Models...............228
6.3.1 Simplex restrictions on Poisson rates......228
6.3.2 Data augmentation................228
6.3.3 MLE via the EM algorithm...........229
6.3.4 Bayes estimation via the DA algorithm .... 230
6.3.5 Life insurance data analysis...........231
6.4 Constrained Binomial Models..............233
6.4.1 Statistical model.................233
6.4.2 A physical particle model............234
6.4.3 MLE via the EM algorithm...........236
6.4.4 Bayes estimation via the DA algorithm .... 239
Problems.........................240
7 Checking Compatibility and Uniqueness 241
7.1 Introduction........................241
7.2 Two Continuous Conditional Distributions:
Product Measurable Space (PMS) ...........243
7.2.1 Several basic notions...............243
7.2.2 A review on existing methods..........244
7.2.3 Two examples ..................246
7.3 Finite Discrete Conditional Distributions: PMS .... 247
7.3.1 The formulation of the problems........248
7.3.2 The connection with quadratic optimization
under box constraints..............248
7.3.3 Numerical examples...............250
7.3.4 Extension to more than two dimensions .... 253
7.3.5 The compatibility of regression function and
conditional distribution.............255
7.3.6 Appendix: S-plus function (lseb)........258
7.3.7 Discussion.....................258
7.4 Two Conditional Distributions: NPMS.........259
7.5 One Marginal and Another Conditional Distribution . 262
7.5.1 A sufficient condition for uniqueness......262
7.5.2 The continuous case...............265
7.5.3 The finite discrete case..............266
7.5.4 The connection with quadratic optimization
under box constraints..............269
Problems .........................271
CONTENTS xiii
A Basic Statistical Distributions and Stochastic
Processes 273
A.I Discrete Distributions..................273
A.2 Continuous Distributions ................275
A.3 Mixture Distributions ..................283
A.4 Stochastic Processes...................285
List of Figures 287
List of Tables 290
List of Acronyms 292
List of Symbols 294
References 298
Author Index 318
Subject Index 323
|
| any_adam_object | 1 |
| author | Tan, Ming T. Tian, Guo-Liang Ng, Kai Wang |
| author_facet | Tan, Ming T. Tian, Guo-Liang Ng, Kai Wang |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 |
| dewey-search | 519.5/42 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035947490 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:07:55Z |
| institution | BVB |
| isbn | 9781420077490 |
| language | English |
| lccn | 2009028155 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018804604 |
| oclc_num | 427757157 |
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| physical | XVIII, 328 S. Ill. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Chapman & Hall |
| record_format | marc |
| series | Chapman & Hall/CRC biostatistics series |
| series2 | Chapman & Hall/CRC biostatistics series |
| spelling | Tan, Ming T. Verfasser aut Bayesian missing data problems EM, data augmentation and noniterative computation Ming T. Tan ; Guo-Liang Tian ; Kai Wang Ng Boca Raton Chapman & Hall 2010 XVIII, 328 S. Ill. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC biostatistics series 32 Includes bibliographical references and index Bayesian statistical decision theory Missing observations (Statistics) Tian, Guo-Liang Verfasser aut Ng, Kai Wang Verfasser aut Chapman & Hall/CRC biostatistics series 32 (DE-604)BV023097394 32 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804604&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tan, Ming T. Tian, Guo-Liang Ng, Kai Wang Bayesian missing data problems EM, data augmentation and noniterative computation Chapman & Hall/CRC biostatistics series Bayesian statistical decision theory Missing observations (Statistics) |
| title | Bayesian missing data problems EM, data augmentation and noniterative computation |
| title_auth | Bayesian missing data problems EM, data augmentation and noniterative computation |
| title_exact_search | Bayesian missing data problems EM, data augmentation and noniterative computation |
| title_full | Bayesian missing data problems EM, data augmentation and noniterative computation Ming T. Tan ; Guo-Liang Tian ; Kai Wang Ng |
| title_fullStr | Bayesian missing data problems EM, data augmentation and noniterative computation Ming T. Tan ; Guo-Liang Tian ; Kai Wang Ng |
| title_full_unstemmed | Bayesian missing data problems EM, data augmentation and noniterative computation Ming T. Tan ; Guo-Liang Tian ; Kai Wang Ng |
| title_short | Bayesian missing data problems |
| title_sort | bayesian missing data problems em data augmentation and noniterative computation |
| title_sub | EM, data augmentation and noniterative computation |
| topic | Bayesian statistical decision theory Missing observations (Statistics) |
| topic_facet | Bayesian statistical decision theory Missing observations (Statistics) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018804604&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023097394 |
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