Monte Carlo methods in Bayesian computation:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 386 S. graph. Darst. |
| ISBN: | 0387989358 |
Staff View
MARC
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| 245 | 1 | 0 | |a Monte Carlo methods in Bayesian computation |c Ming-Hui Chen ; Qi-Man Shao ; Joseph G. Ibrahim |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a XIII, 386 S. |b graph. Darst. | ||
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| 650 | 4 | |a Statistique bayésienne | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Monte Carlo method | |
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Record in the Search Index
| _version_ | 1804127741073686528 |
|---|---|
| adam_text | CONTENTS
PREFACE VI I
1 INTRODUCTION 1
1.1 AIMS 1
1.2 OUTLINE 2
1.3 MOTIVATING EXAMPLES 4
1.4 THE BAYESIAN PARADIGM 14
EXERCISES 15
2 MARKOV CHAIN MONTE CARLO SAMPLING 19
2.1 GIBBS SAMPLER 20
2.2 METROPOLIS-HASTINGS ALGORITHM 23
2.3 HIT-AND-RUN ALGORITHM 26
2.4 MULTIPLE-TRY METROPOLIS ALGORITHM 30
2.5 GROUPING, COLLAPSING, AND REPARAMETERIZATIONS 31
2.5.1 GROUPED AND COLLAPSED GIBBS 31
2.5.2 REPARAMETERIZATIONS: HIERARCHICAL CENTERING AND
RESCALING 34
2.5.3 COLLAPSING AND REPARAMETERIZATION FOR ORDINAL RE-
SPONSE MODELS 35
2.5.4 HIERARCHICAL CENTERING FOR POISSON RANDOM EFFECTS
MODELS 40
2.6 ACCELERATION ALGORITHMS FOR MCMC SAMPLING 42
2.6.1 GROUPED MOVE AND MULTIGRID MONTE CARLO SAM-
PLING 43
2.6.2 COVARIANCE-ADJUSTED MCMC ALGORITHM 45
2.6.3 AN ILLUSTRATION 47
2.7 DYNAMIC WEIGHTING ALGORITHM 52
2.8 TOWARD BLACK-BOX SAMPLING 55
2.9 CONVERGENCE DIAGNOSTICS 59
EXERCISES 63
3 BASIC MONTE CARLO METHODS FOR ESTIMATING POSTERIOR
QUANTITIES 67
3.1 POSTERIOR QUANTITIES 67
3.2 BASIC MONTE CARLO METHODS 68
3.3 SIMULATION STANDARD ERROR ESTIMATION 71
3.3.1 TIME SERIES APPROACH 71
3.3.2 OVERLAPPING BATCH STATISTICS 73
3.4 IMPROVING MONTE CARLO ESTIMATES 77
3.4.1 VARIANCE-REDUCTION MCMC SAMPLING 77
3.4.2 WEIGHTED MONTE CARLO ESTIMATES 81
3.5 CONTROLLING SIMULATION ERRORS 86
APPENDIX 89
EXERCISES 89
4 ESTIMATING MARGINAL POSTERIOR DENSITIES 94
4.1 MARGINAL POSTERIOR DENSITIES 95
4.2 KERNEL METHODS 97
4.3 IWMDE METHODS 98
4.4 ILLUSTRATIVE EXAMPLES 104
4.5 PERFORMANCE STUDY USING THE KULLBACK-LEIBLER DIVERGENCE 107
APPENDIX 117
EXERCISES 121
5 ESTIMATING RATIOS OF NORMALIZING CONSTANTS 124
5.1 INTRODUCTION 124
5.2 IMPORTANCE SAMPLING 125
5.2.1 IMPORTANCE SAMPLING-VERSION 1 126
5.2.2 IMPORTANCE SAMPLING-VERSION 2 126
5.3 BRIDGE SAMPLING 127
5.4 PATH SAMPLING 129
5.4.1 UNIVARIATE PATH SAMPLING 130
5.4.2 MULTIVARIATE PATH SAMPLING 131
5.4.3 CONNECTION BETWEEN PATH SAMPLING AND BRIDGE
SAMPLING 132
5.5 RATIO IMPORTANCE SAMPLING 132
5.5.1 THE METHOD 132
5.5.2 IMPLEMENTATION 135
5.6 A THEORETICAL ILLUSTRATION 138
5.7 COMPUTING SIMULATION STANDARD ERRORS 143
5.8 EXTENSIONS TO DENSITIES WITH DIFFERENT DIMENSIONS .... 145
5.8.1 WHY DIFFERENT DIMENSIONS? 145
5.8.2 GENERAL FORMULATION 146
5.8.3 EXTENSIONS OF THE PREVIOUS MONTE CARLO METHODS 147
5.8.4 GLOBAL OPTIMAL ESTIMATORS 149
5.8.5 IMPLEMENTATION ISSUES 152
5.9 ESTIMATION OF NORMALIZING CONSTANTS AFTER TRANSFORMATION 160
5.10 OTHER METHODS 161
5.10.1 MARGINAL LIKELIHOOD APPROACH 162
5.10.2 REVERSE LOGISTIC REGRESSION 163
5.10.3 THE SAVAGE-DICKEY DENSITY RATIO 164
5.11 AN APPLICATION OF WEIGHTED MONTE CARLO ESTIMATORS . . 165
5.12 DISCUSSION 172
APPENDIX 173
EXERCISES 187
6 MONTE CARLO METHODS FOR CONSTRAINED PARAMETER PROB-
LEMS 191
6.1 CONSTRAINED PARAMETER PROBLEMS 191
6.2 POSTERIOR MOMENTS AND MARGINAL POSTERIOR DENSITIES . . 193
6.3 COMPUTING NORMALIZING CONSTANTS FOR BAYESIAN ESTIMATION 196
6.4 APPLICATIONS 199
6.4.1 THE MEAL, READY-TO-EAT (MRE) MODEL 199
6.4.2 JOB SATISFACTION EXAMPLE 205
6.5 DISCUSSION 208
APPENDIX 208
EXERCISES 211
7 COMPUTING BAYESIAN CREDIBLE AND HPD INTERVALS 213
7.1 BAYESIAN CREDIBLE AND HPD INTERVALS 214
7.2 ESTIMATING BAYESIAN CREDIBLE INTERVALS 216
7.3 ESTIMATING BAYESIAN HPD INTERVALS 218
7.3.1 AN ORDER STATISTICS APPROACH 219
7.3.2 WEIGHTED MONTE CARLO ESTIMATION OF HPD INTERVALS 220
7.4 EXTENSION TO THE CONSTRAINED PARAMETER PROBLEMS . . . 221
7.5 NUMERICAL ILLUSTRATION 223
7.5.1 A SIMULATION STUDY 223
7.5.2 MEAL, READY-TO-EAT (MRE) DATA EXAMPLE .... 224
7.6 DISCUSSION 226
APPENDIX 227
EXERCISES 232
8 BAYESIAN APPROACHES FOR COMPARING NONNESTED MODELS 236
8.1 MARGINAL LIKELIHOOD APPROACHES 237
8.1.1 THE METHOD 237
8.1.2 COMPUTATION 237
8.2 SCALE MIXTURES OF MULTIVARIATE NORMAL LINK MODELS . . . 239
8.2.1 THE MODELS 240
8.2.2 PRIOR DISTRIBUTIONS AND POSTERIOR COMPUTATIONS . 242
8.2.3 MODEL COMPARISON 245
8.2.4 ITEM RESPONSE DATA EXAMPLE 249
8.3 SUPER-MODEL OR SUB-MODEL APPROACHES 250
8.4 CRITERION-BASED METHODS 252
8.4.1 THE L MEASURE 253
8.4.2 THE CALIBRATION DISTRIBUTION 256
8.4.3 BREAST CANCER DATA EXAMPLE 259
EXERCISES 263
9 BAYESIAN VARIABLE SELECTION 267
9.1 VARIABLE SELECTION FOR LOGISTIC REGRESSION MODELS .... 268
9.1.1 MODEL AND NOTATION 268
9.1.2 THE PRIOR DISTRIBUTIONS 269
9.1.3 A GENERALIZATION OF THE PRIORS 270
9.1.4 CHOICES OF PRIOR PARAMETERS 272
9.1.5 PRIOR DISTRIBUTION ON THE MODEL SPACE 273
9.1.6 COMPUTING PRIOR AND POSTERIOR MODEL PROBABILITIES 275
9.2 VARIABLE SELECTION FOR TIME SERIES COUNT DATA MODELS . 282
9.2.1 THE LIKELIHOOD FUNCTION 283
9.2.2 PRIOR DISTRIBUTIONS FOR /3
(M)
284
9.2.3 PRIOR DISTRIBUTION ON THE MODEL SPACE 286
9.2.4 SAMPLING FROM THE POSTERIOR DISTRIBUTION 287
9.2.5 COMPUTATION OF POSTERIOR MODEL PROBABILITIES . . 289
9.3 STOCHASTIC SEARCH VARIABLE SELECTION 293
9.4 BAYESIAN MODEL AVERAGING 297
9.5 REVERSIBLE JUMP MCMC ALGORITHM FOR VARIABLE SELECTION 300
APPENDIX 303
EXERCISES 304
10 OTHER TOPICS 307
10.1 BAYESIAN MODEL ADEQUACY 307
10.1.1 PREDICTIVE APPROACH 307
10.1.2 LATENT RESIDUAL APPROACH 315
10.2 COMPUTING POSTERIOR MODES 320
10.2.1 LINDLEY-SMITH OPTIMIZATION 320
10.2.2 STOCHASTIC APPROXIMATION 323
10.3 BAYESIAN COMPUTATION FOR PROPORTIONAL HAZARDS MODELS 326
10.3.1 MODEL 326
10.3.2 PRIOR DISTRIBUTION FOR H
B
(-) 326
10.3.3 THE LIKELIHOOD FUNCTION 328
10.3.4 PRIOR DISTRIBUTION FOR THE REGRESSION COEFFICIENTS 329
10.3.5 SAMPLING FROM THE POSTERIOR DISTRIBUTION 330
10.4 POSTERIOR SAMPLING FOR MIXTURE OF DIRICHLET PROCESS MODELS 334
10.4.1 CONJUGATE MDP MODELS 336
10.4.2 NONCONJUGATE MDP MODELS 337
10.4.3 MDP IN NORMAL RANDOM EFFECTS MODELS 338
10.4.4 MDP FOR GENERALIZED LINEAR MIXED MODELS ... 341
EXERCISES 353
REFERENCES 356
AUTHOR INDEX 375
SUBJECT INDEX 381
|
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| indexdate | 2024-07-09T18:38:10Z |
| institution | BVB |
| isbn | 0387989358 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008886781 |
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| physical | XIII, 386 S. graph. Darst. |
| publishDate | 2000 |
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| spelling | Chen, Ming-Hui 1961- Verfasser (DE-588)12198978X aut Monte Carlo methods in Bayesian computation Ming-Hui Chen ; Qi-Man Shao ; Joseph G. Ibrahim New York [u.a.] Springer 2000 XIII, 386 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Methode van Bayes gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Statistique bayésienne Bayesian statistical decision theory Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Monte-Carlo-Simulation s 1\p DE-604 Shao, Qi-Man Verfasser aut Ibrahim, Joseph G. Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008886781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chen, Ming-Hui 1961- Shao, Qi-Man Ibrahim, Joseph G. Monte Carlo methods in Bayesian computation Methode van Bayes gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Statistique bayésienne Bayesian statistical decision theory Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Monte-Carlo-Simulation |
| subject_GND | (DE-588)4240945-7 |
| title | Monte Carlo methods in Bayesian computation |
| title_auth | Monte Carlo methods in Bayesian computation |
| title_exact_search | Monte Carlo methods in Bayesian computation |
| title_full | Monte Carlo methods in Bayesian computation Ming-Hui Chen ; Qi-Man Shao ; Joseph G. Ibrahim |
| title_fullStr | Monte Carlo methods in Bayesian computation Ming-Hui Chen ; Qi-Man Shao ; Joseph G. Ibrahim |
| title_full_unstemmed | Monte Carlo methods in Bayesian computation Ming-Hui Chen ; Qi-Man Shao ; Joseph G. Ibrahim |
| title_short | Monte Carlo methods in Bayesian computation |
| title_sort | monte carlo methods in bayesian computation |
| topic | Methode van Bayes gtt Monte Carlo-methode gtt Monte-Carlo, Méthode de Statistique bayésienne Bayesian statistical decision theory Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Monte-Carlo-Simulation |
| topic_facet | Methode van Bayes Monte Carlo-methode Monte-Carlo, Méthode de Statistique bayésienne Bayesian statistical decision theory Monte Carlo method Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008886781&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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