Bayesian theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Wiley
2001
|
| Edition: | Repr. |
| Series: | Wiley series in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 586 S. graph. Darst. |
| ISBN: | 0471924164 |
Staff View
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Record in the Search Index
| _version_ | 1804128769030488064 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1 1.1. THOMAS BAYES 1 1.2. THE SUBJECTIVIST VIEW OF
PROBABILITY 1.3. BAYESIAN STATISTICS IN PERSPECTIVE 3 1.4. AN OVERVIEW
OF BAYESIAN THEORY 5 1.4.1. SCOPE 5 1.4.2. FOUNDATIONS 5 1.4.3.
GENERALISATIONS 6 1.4.4. MODELLING 7 1.4.5. INFERENCE 7 1.4.6.
REMODELLING 8 1.4.7. BASIC FORMULAE 8 1.4.8. NON-BAYESIAN THEORIES 9
1.5. A BAYESIAN READING LIST 9
IMAGE 2
2. FOUNDATIONS 13
2.1. BELIEFS AND ACTIONS 13
2.2. DECISION PROBLEMS 1 6 2.2.1. BASIC ELEMENTS 16 2.2.2. FORMAL
REPRESENTATION 18
2.3. COHERENCE AND QUANTIFICATION 23 2.3. 1 . EVENTS, OPTIONS AND
PREFERENCES 23 2.3.2. COHERENT PREFERENCES 23 2.3.3. QUANTIFICATION 28
2.4. BELIEFS AND PROBABILITIES 33 2.4.1. REPRESENTATION OF BELIEFS 33
2.4.2. REVISION OF BELIEFS AND BAYES THEOREM 38 2.4.3. CONDITIONAL
INDEPENDENCE 45 2.4.4. SEQUENTIAL REVISION OF BELIEFS 47
2.5. ACTIONS AND UTILITIES 49 2.5.1. BOUNDED SETS OF CONSEQUENCES 49
2.5.2. BOUNDED DECISION PROBLEMS 50 2.5.3. GENERAL DECISION PROBLEMS 54
2.6. SEQUENTIAL DECISION PROBLEMS 56
2.6.1. COMPLEX DECISION PROBLEMS 56 2.6.2. BACKWARD INDUCTION 59 2.6.3.
DESIGN OF EXPERIMENTS 63
2.7. INFERENCE AND INFORMATION 67 2.7. 1 . REPORTING BELIEFS AS A
DECISION PROBLEM 67 2.7.2. THE UTILITY OF A PROBABILITY DISTRIBUTION 69
2.7.3. APPROXIMATION AND DISCREPANCY 75
2.7.4. INFORMATION 77
2.8. DISCUSSION AND FURTHER REFERENCES 81 2.8.1. OPERATIONAL DEFINITIONS
81 2.8.2. QUANTITATIVE COHERENCE THEORIES 83 2.8.3. RELATED THEORIES 85
2.8.4. CRITICAL ISSUES 92
IMAGE 3
3. GENERALISATIONS 105
3.1. GENERALISED REPRESENTATION OF BELIEFS 105 3.1.1. MOTIVATION 105
3.1.2. COUNTABLE ADDITIVITY 106
3.2. REVIEW OF PROBABILITY THEORY 109 3.2.1. RANDOM QUANTITIES AND
DISTRIBUTIONS 109 3.2.2. SOME PARTICULAR UNIVARIATE DISTRIBUTIONS 114
3.2.3. CONVERGENCE AND LIMIT THEOREMS 125
3.2.4. RANDOM VECTORS, BAYES THEOREM 127 3.2.5. SOME PARTICULAR
MULTIVARIATE DISTRIBUTIONS 133
3.3. GENERALISED OPTIONS AND UTILITIES 141 3.3.1. MOTIVATION AND
PRELIMINARIES 141 3.3.2. GENERALISED PREFERENCES 145 3.3.3. THE VALUE OF
INFORMATION 147
3.4. GENERALISED INFORMATION MEASURES 150 3.4. 1 . THE GENERAL PROBLEM
OF REPORTING BELIEFS 150 3.4.2. THE UTILITY OF A GENERAL PROBABILITY
DISTRIBUTION 151 3.4.3. GENERALISED APPROXIMATION AND DISCREPANCY 154
3.4.4. GENERALISED INFORMATION 157
3.5. DISCUSSION AND FURTHER REFERENCES 160 3.5.1. THE ROLE OF
MATHEMATICS 160 3.5.2. CRITICAL ISSUES 161
4. MODELLING 165
4.1 STATISTICAL MODELS 165
4.1.1. BELIEFS AND MODELS 1 65
4.2. EXCHANGEABILITY AND RELATED CONCEPTS 1 67
4.2.1. DEPENDENCE AND INDEPENDENCE 167 4.2.2. EXCHANGEABILITY AND
PARTIAL EXCHANGEABILITY 168
4.3. MODELS VIA EXCHANGEABILITY 172 4.3.1. THE BERNOULLI AND BINOMIAL
MODELS 172 4.3.2. THE MULTINOMIAL MODEL 176 4.3.3. THE GENERAL MODEL 177
IMAGE 4
4.4. MODELS VIA INVARIANCE 1 8 1
4.4.1. THE NORMAL MODEL 181 4.4.2. THE MULTIVARIATE NORMAL MODEL 185
4.4.3. THE EXPONENTIAL MODEL 187 4.4.4. THE GEOMETRIC MODEL 189
4.5. MODELS VIA SUFFICIENT STATISTICS 1 90 4.5.1. SUMMARY STATISTICS 190
4.5.2. PREDICTIVE SUFFICIENCY AND PARAMETRIC SUFFICIENCY 191 4.5.3.
SUFFICIENCY AND THE EXPONENTIAL FAMILY 197 4.5.4. INFORMATION MEASURES
AND THE EXPONENTIAL FAMILY 207
4.6. MODELS VIA PARTIAL EXCHANGEABILITY 209 4.6.1. MODELS FOR EXTENDED
DATA STRUCTURES 209 4.6.2. SEVERAL SAMPLES 211 4.6.3. STRUCTURED LAYOUTS
217
4.6.4. COVARIATES 219 4.6.5. HIERARCHICAL MODELS 222
4.7. PRAGMATIC ASPECTS 226
4.7.1. FINITE AND INFINITE EXCHANGEABILITY 226 4.7.2. PARAMETRIC AND
NONPARAMETRIC MODELS 228 4.7.3. MODEL ELABORATION 229 4.7.4. MODEL
SIMPLIFICATION 233 4.7.5. PRIOR DISTRIBUTIONS 234
4.8. DISCUSSION AND FURTHER REFERENCES 235
4.8.1. REPRESENTATION THEOREMS 235 4.8.2. SUBJECTIVITY AND OBJECTIVITY
236 4.8.3. CRITICAL ISSUES 237
5. INFERENCE 241
5.1. THE BAYESIAN PARADIGM 241 5.1.1. OBSERVABLES, BELIEFS AND MODELS
241 5.1.2. THE ROLE OF BAYES THEOREM 242 5.1.3. PREDICTIVE AND
PARAMETRIC INFERENCE 243 5.1.4. SUFFICIENCY, ANCILLARITY AND STOPPING
RULES 247 5.1.5. DECISIONS AND INFERENCE SUMMARIES 255 5.1.6.
IMPLEMENTATION ISSUES 263
IMAGE 5
5.2. CONJUGATE ANALYSIS 265
5.2.1. CONJUGATE FAMILIES 265 5.2.2. CANONICAL CONJUGATE ANALYSIS 269
5.2.3. APPROXIMATIONS WITH CONJUGATE FAMILIES 279
5.3. ASYMPTOTIC ANALYSIS 285 5.3.1. DISCRETE ASYMPTOTICS 286 5.3.2.
CONTINUOUS ASYMPTOTICS 287 5.3.3. ASYMPTOTICS UNDER TRANSFORMATIONS 295
5.4. REFERENCE ANALYSIS 298 5.4.1. REFERENCE DECISIONS 299 5.4.2.
ONE-DIMENSIONAL REFERENCE DISTRIBUTIONS 302 5.4.3. RESTRICTED REFERENCE
DISTRIBUTIONS 316 5.4.4. NUISANCE PARAMETERS 320
5.4.5. MULTIPARAMETER PROBLEMS 333
5.5. NUMERICAL APPROXIMATIONS 339 5.5.1. LAPLACE APPROXIMATION 340
5.5.2. ITERATIVE QUADRATURE 346 5.5.3. IMPORTANCE SAMPLING 348 5.5.4.
SAMPLING-IMPORTANCE-RESAMPLING 350
5.5.5. MARKOV CHAIN MONTE CARLO 353
5.6. DISCUSSION AND FURTHER REFERENCES 356 5.6.1. AN HISTORICAL FOOTNOTE
356 5.6.2. PRIOR IGNORANCE 357 5.6.3. ROBUSTNESS 367
5.6.4. HIERARCHICAL AND EMPIRICAL BAYES 371 5.6.5. FURTHER
METHODOLOGICAL DEVELOPMENTS 373 5.6.6. CRITICAL ISSUES 374
6. REMODELLING 377
6.1. MODEL COMPARISON 377 .1. RANGES OF MODELS 377 .2. PERSPECTIVES ON
MODEL COMPARISON 383 .3. MODEL COMPARISON AS A DECISION PROBLEM 386 .4.
ZERO-ONE UTILITIES AND BAYES FACTORS 389
.5. GENERAL UTILITIES 395 .6. APPROXIMATION BY CROSS-VALIDATION 403 .7.
COVARIATE SELECTION 407
IMAGE 6
6.2. MODEL REJECTION 409
6.2.1. MODEL REJECTION THROUGH MODEL COMPARISON 409 6.2.2. DISCREPANCY
MEASURES FOR MODEL REJECTION 412 6.2.3. ZERO-ONE DISCREPANCIES 413
6.2.4. GENERAL DISCREPANCIES 415
6.3. DISCUSSION AND FURTHER REFERENCES 417 6.3.1. OVERVIEW 417 6.3.2.
MODELLING AND REMODELLING 418 6.3.3. CRITICAL ISSUES 418
A. SUMMARY OF BASIC FORMULAE 427
A.I. PROBABILITY DISTRIBUTIONS 427
A.2. INFERENTIAL PROCESSES 436
B. NON-BAYESIAN THEORIES 443
B.I. OVERVIEW 443
B.2. ALTERNATIVE APPROACHES 445 B.2.1. CLASSICAL DECISION THEORY 445
B.2.2. FREQUENTIST PROCEDURES 449 B.2.3. LIKELIHOOD INFERENCE 454
B.2.4. FIDUCIAL AND RELATED THEORIES 456
B.3. STYLISED INFERENCE PROBLEMS 460 B.3.1. POINT ESTIMATION 460 B.3.2.
INTERVAL ESTIMATION 465 B.3.3. HYPOTHESIS TESTING 469
B.3.4. SIGNIFICANCE TESTING 475
B.4. COMPARATIVE ISSUES 478 B.4.1. CONDITIONAL AND UNCONDITIONAL
INFERENCE 478 B.4.2. NUISANCE PARAMETERS AND MARGINALISATION 479 B.4.3.
APPROACHES TO PREDICTION 482 B.4.4. ASPECTS OF ASYMPTOTICS 485
B.4.5. MODEL CHOICE CRITERIA 486
REFERENCES 489
SUBJECT INDEX 555
AUTHOR INDEX 573
|
| any_adam_object | 1 |
| author | Bernardo, José M. Smith, Adrian F. M. 1946- |
| author_GND | (DE-588)12467464X |
| author_facet | Bernardo, José M. Smith, Adrian F. M. 1946- |
| author_role | aut aut |
| author_sort | Bernardo, José M. |
| author_variant | j m b jm jmb a f m s afm afms |
| building | Verbundindex |
| bvnumber | BV013924277 |
| classification_tum | MAT 622f MAT 624f |
| ctrlnum | (OCoLC)248557541 (DE-599)BVBBV013924277 |
| dewey-full | 519.542 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.542 |
| dewey-search | 519.542 |
| dewey-sort | 3519.542 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Repr. |
| format | Book |
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| id | DE-604.BV013924277 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:30Z |
| institution | BVB |
| isbn | 0471924164 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009528238 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | XIV, 586 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spelling | Bernardo, José M. Verfasser aut Bayesian theory José M. Bernardo ; Adrian F. M. Smith Repr. Chichester u.a. Wiley 2001 XIV, 586 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics CD-ROM (DE-588)4139307-7 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s CD-ROM (DE-588)4139307-7 s DE-604 Bayes-Verfahren (DE-588)4204326-8 s 1\p DE-604 Entscheidungstheorie (DE-588)4138606-1 s 2\p DE-604 Smith, Adrian F. M. 1946- Verfasser (DE-588)12467464X aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009528238&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bernardo, José M. Smith, Adrian F. M. 1946- Bayesian theory CD-ROM (DE-588)4139307-7 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4139307-7 (DE-588)4204326-8 (DE-588)4138606-1 (DE-588)4144220-9 |
| title | Bayesian theory |
| title_auth | Bayesian theory |
| title_exact_search | Bayesian theory |
| title_full | Bayesian theory José M. Bernardo ; Adrian F. M. Smith |
| title_fullStr | Bayesian theory José M. Bernardo ; Adrian F. M. Smith |
| title_full_unstemmed | Bayesian theory José M. Bernardo ; Adrian F. M. Smith |
| title_short | Bayesian theory |
| title_sort | bayesian theory |
| topic | CD-ROM (DE-588)4139307-7 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | CD-ROM Bayes-Verfahren Entscheidungstheorie Bayes-Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009528238&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bernardojosem bayesiantheory AT smithadrianfm bayesiantheory |