Bayes and empirical Bayes methods for data analysis
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| Späterer Titel: | Carlin, Bradley P. Bayesian methods for data analysis |
|---|---|
| Hauptverfasser: | , |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Texts in statistical science series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Bayes and empirical Bayes methods for data analysis |c Bradley P. Carlin and Thomas A. Louis |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2000 | |
| 300 | |a XVII, 419 S. |b graph. Darst. | ||
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| _version_ | 1823052231446888448 |
| adam_text | IMAGE 1
CONTENTS
PREFACE TO THE SECOND EDITION XIII
PREFACE TO THE FIRST EDITION XV
1 APPROACHES FOR STATISTICAL INFERENCE 1
1.1 INTRODUCTION 1
1.2 MOTIVATING VIGNETTES 2
1.2.1 PERSONAL PROBABILITY 2
1.2.2 MISSING DATA 2
1.2.3 BIOASSAY 3
1.2.4 ATTENUATION ADJUSTMENT 4
1.3 DEFINING THE APPROACHES 4
1.4 THE BAYES-FREQUENTIST CONTROVERSY 6
1.5 SOME BASIC BAYESIAN MODELS 10
1.5.1 A GAUSSIAN/GAUSSIAN (NORMAL/NORMAL) MODEL 11 1.5.2 A BETA/BINOMIAL
MODEL 11
1.6 EXERCISES 13
2 THE BAYES APPROACH 17
2.1 INTRODUCTION 17
2.2 PRIOR DISTRIBUTIONS 22
2.2.1 ELICITED PRIORS 23
2.2.2 CONJUGATE PRIORS 25
2.2.3 NONINFORMATIVE PRIORS 28
2.2.4 OTHER PRIOR CONSTRUCTION METHODS 31
2.3 BAYESIAN INFERENCE 32
2.3.1 POINT ESTIMATION 32
2.3.2 INTERVAL ESTIMATION 35
2.3.3 HYPOTHESIS TESTING AND BAYES FACTORS 38
2.3.4 EXAMPLE: CONSUMER PREFERENCE DATA 42
2.4 MODEL ASSESSMENT 46
2.4.1 DIAGNOSTIC MEASURES 46
IMAGE 2
2.4.2 MODEL AVERAGING 49
2.5 NONPARAMETRIC METHODS 51
2.6 EXERCISES 53
THE EMPIRICAL BAYES APPROACH 57
3.1 INTRODUCTION 57
3.2 NONPARAMETRIC EB (NPEB) POINT ESTIMATION 58
3.2.1 COMPOUND SAMPLING MODELS 58
3.2.2 SIMPLE NPEB (ROBBINS METHOD) 59
3.2.3 EXAMPLE: ACCIDENT DATA 60
3.3 PARAMETRIC EB (PEB) POINT ESTIMATION 62
3.3.1 GAUSSIAN/GAUSSIAN MODELS 62
3.3.2 BETA/BINOMIAL MODEL 67
3.3.3 EB PERFORMANCE OF THE PEB 69
3.3.4 STEIN ESTIMATION 70
3.4 COMPUTATION VIA THE EM ALGORITHM 74
3.4.1 EM FOR PEB 74
3.4.2 COMPUTING THE OBSERVED INFORMATION 76
3.4.3 EM FOR NPEB 77
3.4.4 SPEEDING CONVERGENCE AND GENERALIZATIONS 77 3.5 INTERVAL
ESTIMATION 78
3.5.1 MORRIS APPROACH 79
3.5.2 MARGINAL POSTERIOR APPROACH 80
3.5.3 BIAS CORRECTION APPROACH 82
3.6 GENERALIZATION TO REGRESSION STRUCTURES 85
3.7 EXERCISES 86
PERFORMANCE OF BAYES PROCEDURES 89
4.1 BAYESIAN PROCESSING 90
4.1.1 UNIVARIATE STRETCHING WITH A TWO-POINT PRIOR 90 4.1.2 MULTIVARIATE
GAUSSIAN MODEL 90
4.2 FREQUENTIST PERFORMANCE: POINT ESTIMATES 92
4.2.1 GAUSSIAN/GAUSSIAN MODEL 92
4.2.2 BETA/BINOMIAL MODEL 94
4.2.3 GENERALIZATION 97
4.3 FREQUENTIST PERFORMANCE: CONFIDENCE INTERVALS 98
4.3.1 BETA/BINOMIAL MODEL 98
4.3.2 FIELLER-CREASY PROBLEM 103
4.4 EMPIRICAL BAYES PERFORMANCE 108
4.4.1 POINT, ESTIMATION 108
4.4.2 INTERVAL ESTIMATION 111
4.5 DESIGN OF EXPERIMENTS 114
4.5.1 BAYESIAN DESIGN FOR FREQUENTIST ANALYSIS 114
4.5.2 BAYESIAN DESIGN FOR BAYESIAN ANALYSIS 116
IMAGE 3
4.6 EXERCISES 1 19
BAYESIAN COMPUTATION 121
5.1 INTRODUCTION 121
5.2 ASYMPTOTIC METHODS 122
5.2.1 NORMAL APPROXIMATION 122
5.2.2 LAPLACE S METHOD 124
5.3 NONITERATIVE MONTE CARLO METHODS 129
5.3.1 DIRECT SAMPLING 129
5.3.2 INDIRECT METHODS 131
5.4 MARKOV CHAIN MONTE CARLO METHODS 137
5.4.1 SUBSTITUTION SAMPLING AND DATA AUGMENTATION 137 5.4.2 GIBBS
SAMPLING 141
5.4.3 METROPOLIS-HASTINGS ALGORITHM 152
5.4.4 HYBRID FORMS AND OTHER ALGORITHMS 159
5.4.5 VARIANCE ESTIMATION 170
5.4.6 CONVERGENCE MONITORING AND DIAGNOSIS 172
5.5 EXERCISES 183
MODEL CRITICISM AND SELECTION 193
6.1 BAYESIAN ROBUSTNESS 194
6.1.1 SENSITIVITY ANALYSIS 194
6.1.2 PRIOR PARTITIONING 199
6.2 MODEL ASSESSMENT 204
6.3 BAYES FACTORS VIA MARGINAL DENSITY ESTIMATION 206
6.3.1 DIRECT METHODS 207
6.3.2 USING GIBBS SAMPLER OUTPUT 208
6.3.3 USING METROPOLIS-HASTINGS OUTPUT 210
6.4 BAYES FACTORS VIA SAMPLING OVER THE MODEL SPACE 211
6.4.1 PRODUCT SPACE SEARCH 213
6.4.2 METROPOLIZED PRODUCT SPACE SEARCH 215
6.4.3 REVERSIBLE JUMP MCMC 216
6.4.4 USING PARTIAL ANALYTIC STRUCTURE 217
6.5 OTHER MODEL SELECTION METHODS 219
6.5.1 PENALIZED LIKELIHOOD CRITERIA 220
6.5.2 PREDICTIVE MODEL SELECTION 223
6.6 EXERCISES 225
SPECIAL METHODS AND MODELS 229
7.1 ESTIMATING HISTOGRAMS AND RANKS 229
7.1.1 MODEL AND INFERENTIAL GOALS 230
7.1.2 TRIPLE GOAL ESTIMATES 232
7.1.3 SMOOTHING AND ROBUSTNESS 234
7.2 ORDER RESTRICTED INFERENCE 237
IMAGE 4
7.3 NONLINEAR MODELS 239
7.4 LONGITUDINAL DATA MODELS 242
7.5 CONTINUOUS AND CATEGORICAL TIME SERIES 244
7.6 SURVIVAL ANALYSIS AND FRAILTY MODELS 246
7.6.1 STATISTICAL MODELS 246
7.6.2 TREATMENT EFFECT PRIOR DETERMINATION 247
7.6.3 COMPUTATION AND ADVANCED MODELS 248
7.7 SEQUENTIAL ANALYSIS 249
7.7.1 MODEL AND LOSS STRUCTURE 250
7.7.2 BACKWARD INDUCTION 252
7.7.3 FORWARD SAMPLING 252
7.8 SPATIAL AND SPATIO-TEMPORAL MODELS 255
7.8.1 POINT SOURCE DATA MODELS 256
7.8.2 REGIONAL SUMMARY DATA MODELS 259
7.9 EXERCISES 264
8 CASE STUDIES 275
8.1 ANALYSIS OF LONGITUDINAL AIDS DATA 276
8.1.1 INTRODUCTION AND BACKGROUND 276
8.1.2 MODELING OF LONGITUDINAL CD4 COUNTS 277
8.1.3 CD4 RESPONSE TO TREATMENT AT TWO MONTHS 286 8.1.4 SURVIVAL
ANALYSIS 287
8.1.5 DISCUSSION 289
8.2 ROBUST ANALYSIS OF CLINICAL TRIALS 290
8.2.1 CLINICAL BACKGROUND 290
8.2.2 INTERIM MONITORING 290
8.2.3 PRIOR ROBUSTNESS AND PRIOR SCOPING 295
8.2.4 SEQUENTIAL DECISION ANALYSIS 301
8.2.5 DISCUSSION 304
8.3 SPATIO-TEMPORAL MAPPING OF LUNG CANCER RATES 305
8.3.1 INTRODUCTION 305
8.3.2 DATA AND MODEL DESCRIPTION 307
8.3.3 COMPUTATIONAL CONSIDERATIONS 309
8.3.4 MODEL FITTING, VALIDATION, AND COMPARISON 309 8.3.5 DISCUSSION 315
APPENDICES 319
A DISTRIBUTIONAL CATALOG 321
A.I DISCRETE 321
A. 1.1 UNIVARIATE 321
A.1.2 MULTIVARIATE 323
A.2 CONTINUOUS 323
A.2.1 UNIVARIATE 323
IMAGE 5
A.2.2 MULTIVARIATE 327
B DECISION THEORY 329
B.I INTRODUCTION 329
B.I.I RISK AND ADMISSIBILITY 330
B.I.2 UNBIASED RULES 331
B.I.3 BAYES RULES 332
B.I.4 MINIMAX RULES 334
B.2 PROCEDURE EVALUATION AND OTHER UNIFYING CONCEPTS 335 B.2.1 MEAN
SQUARED ERROR 335
B.2.2 THE VARIANCE-BIAS TRADEOFF 335
B.3 OTHER LOSS FUNCTIONS 336
B.3.1 GENERALIZED ABSOLUTE LOSS 337
B.3.2 TESTING WITH A DISTANCE PENALTY 337
B.3.3 A THRESHOLD LOSS FUNCTION 337
B.4 MULTIPLICITY 338
B.5 MULTIPLE TESTING 339
B.5.1 ADDITIVE LOSS 339
B.5.2 NON-ADDITIVE LOSS 340
B.6 EXERCISES 341
C SOFTWARE GUIDE 345
C.I PRIOR ELICITATION 346
C.2 RANDOM EFFECTS MODELS/EMPIRICAL BAYES ANALYSIS 347 C.3 BAYESIAN
ANALYSIS 351
C.3.1 SPECIAL PURPOSE PROGRAMS 352
C.3.2 TEACHING PROGRAMS 356
C.3.3 MARKOV CHAIN MONTE CARLO PROGRAMS 357
D ANSWERS TO SELECTED EXERCISES 363
REFERENCES 381
AUTHOR INDEX 407
SUBJECT INDEX 413
|
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| id | DE-604.BV013567089 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T16:44:36Z |
| institution | BVB |
| isbn | 1584881704 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009266249 |
| oclc_num | 43859506 |
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| physical | XVII, 419 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Texts in statistical science series |
| spellingShingle | Carlin, Bradley P. Louis, Thomas A. 1944- Bayes and empirical Bayes methods for data analysis Besliskunde gtt Data-analyse gtt Informatique Methode van Bayes gtt Statistique bayésienne Statistique bayésienne ram Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4204326-8 |
| title | Bayes and empirical Bayes methods for data analysis |
| title_auth | Bayes and empirical Bayes methods for data analysis |
| title_exact_search | Bayes and empirical Bayes methods for data analysis |
| title_full | Bayes and empirical Bayes methods for data analysis Bradley P. Carlin and Thomas A. Louis |
| title_fullStr | Bayes and empirical Bayes methods for data analysis Bradley P. Carlin and Thomas A. Louis |
| title_full_unstemmed | Bayes and empirical Bayes methods for data analysis Bradley P. Carlin and Thomas A. Louis |
| title_new | Carlin, Bradley P. Bayesian methods for data analysis |
| title_short | Bayes and empirical Bayes methods for data analysis |
| title_sort | bayes and empirical bayes methods for data analysis |
| topic | Besliskunde gtt Data-analyse gtt Informatique Methode van Bayes gtt Statistique bayésienne Statistique bayésienne ram Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Besliskunde Data-analyse Informatique Methode van Bayes Statistique bayésienne Bayesian statistical decision theory Datenanalyse Bayes-Verfahren |
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