Bayes and empirical Bayes methods for data analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
Chapman & Hall
1997
|
| Edition: | Repr. |
| Series: | Monographs on statistics and applied probability
69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 399 S. graph. Darst. |
| ISBN: | 0412056119 |
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MARC
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Record in the Search Index
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| adam_text | BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS BRADLEY P. CARLIN
ASSOCIATE PROFESSOR, DIVISION OF BIOSTATISTICS, SCHOOL OF PUBLIC HEALTH,
UNIVERSITY OF MINNESOTA, MINNEAPOLIS, USA AND THOMAS A. LOUIS PROFESSOR
AND HEAD OF DEPARTMENT, DIVISION OF BIOSTATISTICS, SCHOOL OF PUBLIC
HEALTH, UNIVERSITY OF MINNESOTA, MINNEAPOLIS, USA CHAPMAN & HALL LONDON
* WEINHEIM * NEW YORK * TOKYO * MELBOURNE * MADRAS CONTENTS PREFACE XIII
1 PROCEDURES AND THEIR PROPERTIES 1 1.1 INTRODUCTION AND MOTIVATION 1
1.2 STRUCTURES FOR INFERENCE 6 1.3 THE GENERAL DECISION PROBLEM 7 1.3.1
RISK AND ADMISSIBILITY 9 1.3.2 UNBIASED RULES 10 1.3.3 BAYES RULES 12
1.3.4 MINIMAX RULES 14 1.4 PROCEDURE EVALUATION AND OTHER UNIFYING
CONCEPTS 14 1.4.1 MEAN SQUARED ERROR 15 1.4.2 THE VARIANCE-BIAS TRADEOFF
15 1.5 EXERCISES 17 2 THE BAYES APPROACH 21 2.1 INTRODUCTION 21 2.2
PRIOR DISTRIBUTIONS 26 2.2.1 ELICITED PRIORS 27 2.2.2 CONJUGATE PRIORS
30 2.2.3 NONINFORMATIVE PRIORS 33 2.2.4 OTHER PRIOR CONSTRUCTION METHODS
37 2.3 BAYESIAN INFERENCE 38 2.3.1 POINT ESTIMATION 39 2.3.2 INTERVAL
ESTIMATION 42 2.3.3 HYPOTHESIS TESTING AND BAYES FACTORS 45 2.3.4
EXAMPLE: CONSUMER PREFERENCE DATA 50 2.4 MODEL ASSESSMENT . 54 2.4.1
DIAGNOSTIC MEASURES 54 2.4.2 MODEL AVERAGING 57 2.5 NONPARAMETRIC
METHODS 59 VIII CONTENTS 2.6 EXERCISES 62 3 THE EMPIRICAL BAYES APPROACH
67 3.1 INTRODUCTION 67 3.2 NONPARAMETRIC EB POINT ESTIMATION 68 3.2.1
COMPOUND SAMPLING MODELS 68 3.2.2 SIMPLE NPEB (ROBBINS METHOD) 69 3.2.3
ESTIMATION OF THE PRIOR (NPML METHOD) 71 3.2.4 EXAMPLE: ACCIDENT DATA 72
3.3 PARAMETRIC EB POINT ESTIMATION 74 3.3.1 GAUSSIAN/GAUSSIAN MODELS 75
3.3.2 BETA/BINOMIAL MODEL 80 3.3.3 EB PERFORMANCE OF THE PEB 82 3.3.4
STEIN ESTIMATION 84 3.4 COMPUTATION VIA THE EM ALGORITHM 89 3.5 INTERVAL
ESTIMATION 93 3.5.1 MORRIS APPROACH 95 3.5.2 MARGINAL POSTERIOR
APPROACH 95 3.5.3 BIAS CORRECTION APPROACH 98 3.6 GENERALIZATION TO
REGRESSION STRUCTURES 100 3.7 EXERCISES 102 4 PERFORMANCE OF BAYES
PROCEDURES 107 4.1 BAYESIAN PROCESSING 108 4.1.1 UNIVARIATE STRETCHING
WITH A TWO-POINT PRIOR 108 4.1.2 MULTIVARIATE GAUSSIAN MODEL 109 4.2
FREQUENTIST PERFORMANCE: POINT ESTIMATES 110 4.2.1 GAUSSIAN/GAUSSIAN
MODEL 111 4.2.2 BETA/BINOMIAL MODEL 113 4.2.3 GENERALIZATION 116 4.3
FREQUENTIST PERFORMANCE: CONFIDENCE INTERVALS 117 4.3.1 BETA/BINOMIAL
MODEL 117 4.3.2 FIELLER-CREASY PROBLEM 124 4.4 EMPIRICAL BAYES
PERFORMANCE 128 4.4.1 POINT ESTIMATION 129 4.4.2 INTERVAL ESTIMATION 132
4.5 DESIGN OF EXPERIMENTS 135 4.5.1 BAYESIAN DESIGN FOR BAYESIAN
ANALYSIS 135 4.5.2 BAYESIAN DESIGN FOR FREQUENTIST ANALYSIS 137 4.6
EXERCISES 139 CONTENTS IX 5 BAYESIAN COMPUTATION 141 5.1 INTRODUCTION
141 5.2 ASYMPTOTIC METHODS 142 5.2.1 NORMAL APPROXIMATION 142 ~- 5.2.2
LAPLACE S METHOD 145 5.3 NONITERATIVE MONTE CARLO METHODS 150 5.3.1
DIRECT SAMPLING 150 5.3.2 INDIRECT METHODS 152 5.4 MARKOV CHAIN MONTE
CARLO METHODS 159 5.4.1 SUBSTITUTION SAMPLING AND DATA AUGMENTA- TION
159 5.4.2 GIBBS SAMPLING 163 5.4.3 METROPOLIS-HASTINGS ALGORITHM 173
5.4.4 HYBRID FORMS AND OTHER ALGORITHMS 180 5.4.5 CONVERGENCE MONITORING
AND ACCELERATION 185 5.5 EXERCISES 197 6 MODEL CRITICISM AND SELECTION
205 6.1 BAYESIAN ROBUSTNESS 206 6.1.1 SENSITIVITY ANALYSIS 206 6.1.2
PRIOR PARTITIONING 212 6.2 MODEL ASSESSMENT 218 6.3 BAYES FACTORS 220
6.3.1 DIRECT METHODS , 221 6.3.2 MARGINAL DENSITIES FROM THE GIBBS
SAMPLER 223 6.3.3 SAMPLING OVER MODEL AND PARAMETER SPACE 225 6.3.4
SAMPLING OVER THE MODEL SPACE ALONE 229 6.4 PREDICTIVE MODEL SELECTION
230 6.5 EXERCISES 233 7 SPECIAL METHODS AND MODELS 237 7.1 ENSEMBLE
ESTIMATES 237 7.2 ORDER RESTRICTED INFERENCE 246 7.3 NONLINEAR MODELS
247 7.4 LONGITUDINAL DATA MODELS 251 7.5 CONTINUOUS AND CATEGORICAL TIME
SERIES 253 7.6 SURVIVAL ANALYSIS AND FRAILTY MODELS 255 7.6.1
STATISTICAL MODELS 256 7.6.2 TREATMENT EFFECT PRIOR DETERMINATION 257
7.6.3 COMPUTATION AND ADVANCED MODELS 258 7.7 SPATIAL AND
SPATIO-TEMPORAL MODELS 260 X CONTENTS 7.8 EXERCISES 265 8 CASE STUDIES
273 8.1 ANALYSIS OF LONGITUDINAL AIDS DATA 274 8.1.1 INTRODUCTION AND
BACKGROUND 274 8.1.2 MODELING OF LONGITUDINAL CD4 COUNTS 275 8.1.3 CD4
RESPONSE TO TREATMENT AT TWO MONTHS 285 8.1.4 SURVIVAL ANALYSIS 287
8.1.5 DISCUSSION 289 8.2 ROBUST ANALYSIS OF CLINICAL TRIALS 289 8.2.1
CLINICAL BACKGROUND 289 8.2.2 INTERIM MONITORING 290 8.2.3 PRIOR
ROBUSTNESS AND PRIOR SCOPING 296 8.2.4 DISCUSSION 302 8.3
SPATIO-TEMPORAL MAPPING OF LUNG CANCER RATES 303 8.3.1 INTRODUCTION 303
8.3.2 DATA AND MODEL DESCRIPTION 305 8.3.3 COMPUTATIONAL CONSIDERATIONS
307 8.3.4 MODEL FITTING, VALIDATION AND COMPARISON 308 8.3.5 DISCUSSION
315 APPENDICES 317 A DISTRIBUTIONAL CATALOG 319 A.I DISCRETE 319 A. 1.1
UNIVARIATE 319 A.1.2 MULTIVARIATE 321 A.2 CONTINUOUS 321 A.2.1
UNIVARIATE 321 A.2.2 MULTIVARIATE 325 B SOFTWARE GUIDE 327 B.I PRIOR
ELICITATION 328 B.2 RANDOM EFFECTS MODELS/EMPIRICAL BAYES ANALYSIS 330
B.3 BAYESIAN ANALYSIS 334 B.3.1 EARLY DEVELOPMENTS 335 B.3.2 SPECIAL
PURPOSE PROGRAMS 336 B.3.3 TEACHING PROGRAMS 341 B.3.4 MARKOV CHAIN
MONTE CARLO PROGRAMS 342 C ANSWERS TO SELECTED EXERCISES 349 CONTENTS XI
REFERENCES 363 AUTHOR INDEX 387 SUBJECT INDEX 393
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | Repr. |
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| indexdate | 2024-07-09T18:07:19Z |
| institution | BVB |
| isbn | 0412056119 |
| language | English |
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| physical | XVI, 399 S. graph. Darst. |
| publishDate | 1997 |
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| publisher | Chapman & Hall |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Carlin, Bradley P. Verfasser (DE-588)134074505 aut Bayes and empirical Bayes methods for data analysis Bradley P. Carlin and Thomas A. Louis Repr. London u.a. Chapman & Hall 1997 XVI, 399 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 69 Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Bayes-Verfahren (DE-588)4204326-8 s DE-604 Louis, Thomas A. 1944- Verfasser (DE-588)112468853 aut Monographs on statistics and applied probability 69 (DE-604)BV002494005 69 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007586031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carlin, Bradley P. Louis, Thomas A. 1944- Bayes and empirical Bayes methods for data analysis Monographs on statistics and applied probability 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_short | Bayes and empirical Bayes methods for data analysis |
| title_sort | bayes and empirical bayes methods for data analysis |
| topic | Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Bayesian statistical decision theory Datenanalyse Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007586031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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