The Bayesian choice: from decision-theoretic foundations to computational implementation
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
New York [u.a.]
Springer
2001
|
| Edition: | 2. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 531 - 579 |
| Physical Description: | XXII, 604 S. graph. Darst. |
| ISBN: | 0387952314 9780387952314 |
Staff View
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Record in the Search Index
| _version_ | 1804128643391160320 |
|---|---|
| adam_text | CHRISTIAN P. ROBERT THE BAYESIAN CHOICE FROM DECISION-THEORETIC
FOUNDATIONS TO COMPUTATIONAL IMPLEMENTATION SECOND EDITION WITH 23
ILLUSTRATIONS ^SPRINGER CONTENTS PREFACE TO THE SECOND EDITION VII
PREFACE TO THE FIRST EDITION XI LIST OF TABLES XXI LIST OF FIGURES XXIII
1 INTRODUCTION 1 1.1 STATISTICAL PROBLEMS AND STATISTICAL MODELS 1 1.2
THE BAYESIAN PARADIGM AS A DUALITY PRINCIPLE 8 1.3 LIKELIHOOD PRINCIPLE
AND SUFFICIENCY PRINCIPLE 13 1.3.1 SUFFICIENCY 13 1.3.2 THE LIKELIHOOD
PRINCIPLE 15 1.3.3 DERIVATION OF THE LIKELIHOOD PRINCIPLE 18 1.3.4
IMPLEMENTATION OF THE LIKELIHOOD PRINCIPLE 19 1.3.5 MAXIMUM LIKELIHOOD
ESTIMATION 20 1.4 PRIOR AND POSTERIOR DISTRIBUTIONS 22 1.5 IMPROPER
PRIOR DISTRIBUTIONS 26 1.6 THE BAYESIAN CHOICE 31 1.7 EXERCISES 31 1.8
NOTES 45 2 DECISION-THEORETIC FOUNDATIONS 51 2.1 EVALUATING ESTIMATORS
51 2.2 EXISTENCE OF A UTILITY FUNCTION 54 2.3 UTILITY AND LOSS 60 2.4
TWO OPTIMALITIES: MINIMAXITY AND ADMISSIBILITY 65 2.4.1 RANDOMIZED
ESTIMATORS 65 2.4.2 MINIMAXITY 66 2.4.3 EXISTENCE OF MINIMAX RULES AND
MAXIMIN STRATEGY 69 2.4.4 ADMISSIBILITY 74 2.5 USUAL LOSS FUNCTIONS . 77
2.5.1 THE QUADRATIC LOSS 77 2.5.2 THE ABSOLUTE ERROR LOSS 79 2.5.3 THE
0-1 LOSS 80 2.5.4 INTRINSIC LOSSES 81 2.6 2.7 2.8 CRITICISMS EXERCISES
NOTES AND CONTENTS ALTERNATIVES 83 85 96 FROM PRIOR INFORMATION TO PRIOR
DISTRIBUTIONS 105 3.1 THE DIFFICULTY IN SELECTING A PRIOR DISTRIBUTION
105 3.2 SUBJECTIVE DETERMINATION AND APPROXIMATIONS 106 3.2.1 EXISTENCE
106 3.2.2 APPROXIMATIONS TO THE PRIOR DISTRIBUTION 108 3.2.3 MAXIMUM
ENTROPY PRIORS 109 3.2.4 PARAMETRIC APPROXIMATIONS 111 3.2.5 OTHER
TECHNIQUES 113 3.3 CONJUGATE PRIORS 113 3.3.1 INTRODUCTION 113 3.3.2
JUSTIFICATIONS 115 3.3.3 EXPONENTIAL FAMILIES 115 3.3.4 CONJUGATE
DISTRIBUTIONS FOR EXPONENTIAL FAMILIES 120 3.4 CRITICISMS AND EXTENSIONS
123 3.5 NONINFORMATIVE PRIOR DISTRIBUTIONS 127 3.5.1 LAPLACE S PRIOR 127
3.5.2 INVARIANT PRIORS 129 3.5.3 THE JEFFREYS PRIOR 129 3.5.4 REFERENCE
PRIORS 133 3.5.5 MATCHING PRIORS 137 3.5.6 OTHER APPROACHES 140 3.6
POSTERIOR VALIDATION AND ROBUSTNESS 141 3.7 EXERCISES 144 3.8 NOTES 158
BAYESIAN POINT ESTIMATION 165 4.1 BAYESIAN INFERENCE 165 4.1.1
INTRODUCTION 165 4.1.2 MAP ESTIMATOR 166 4.1.3 LIKELIHOOD PRINCIPLE 167
4.1.4 RESTRICTED PARAMETER SPACE 168 4.1.5 PRECISION OF THE BAYES
ESTIMATORS 170 4.1.6 PREDICTION 171 4.1.7 BACK TO DECISION THEORY 173
4.2 BAYESIAN DECISION THEORY 173 4.2.1 BAYES ESTIMATORS 173 4.2.2
CONJUGATE PRIORS 175 4.2.3 LOSS ESTIMATION 178 4.3 SAMPLING MODELS 180
4.3.1 LAPLACE SUCCESSION RULE 180 4.3.2 THE TRAMCAR PROBLEM 181 4.3.3
CAPTURE-RECAPTURE MODELS 182 CONTENTS XVII 4.4 THE PARTICULAR CASE OF
THE NORMAL MODEL 186 4.4.1 INTRODUCTION 186 4.4.2 ESTIMATION OF VARIANCE
187 4.4.3 LINEAR MODELS AND G-PRIORS 190 4.5 DYNAMIC MODELS 193 4.5.1
INTRODUCTION 193 4.5.2 THE AR MODEL 196 4.5.3 THE MA MODEL 198 4.5.4 THE
ARMA MODEL 201 4.6 EXERCISES 201 4.7 NOTES 216 TESTS AND CONFIDENCE
REGIONS 223 5.1 INTRODUCTION 223 5.2 A FIRST APPROACH TO TESTING THEORY
224 5.2.1 DECISION-THEORETIC TESTING 224 5.2.2 THE BAYES FACTOR 227
5.2.3 MODIFICATION OF THE PRIOR 229 5.2.4 POINT-NULL HYPOTHESES 230
5.2.5 IMPROPER PRIORS 232 5.2.6 PSEUDO-BAYES FACTORS 236 5.3 COMPARISONS
WITH THE CLASSICAL APPROACH 242 5.3.1 UMP AND UMPU TESTS 242 5.3.2 LEAST
FAVORABLE PRIOR DISTRIBUTIONS 245 5.3.3 CRITICISMS 247 5.3.4 THE
P-VALUES 249 5.3.5 LEAST FAVORABLE BAYESIAN ANSWERS 251 5.3.6 THE
ONE-SIDED CASE 254 5.4 A SECOND DECISION-THEORETIC APPROACH 256 5.5
CONFIDENCE REGIONS 259 5.5.1 CREDIBLE INTERVALS 260 5.5.2 CLASSICAL
CONFIDENCE INTERVALS 263 5.5.3 DECISION-THEORETIC EVALUATION OF
CONFIDENCE SETS 264 5.6 EXERCISES 267 5.7 NOTES 279 BAYESIAN
CALCULATIONS 285 6.1 IMPLEMENTATION DIFFICULTIES 285 6.2 CLASSICAL
APPROXIMATION METHODS 293 6.2.1 NUMERICAL INTEGRATION 293 6.2.2 MONTE
CARLO METHODS 294 6.2.3 LAPLACE ANALYTIC APPROXIMATION 298 6.3 MARKOV
CHAIN MONTE CARLO METHODS 301 6.3.1 MCMC IN PRACTICE 302 6.3.2
METROPOLIS-HASTINGS ALGORITHMS 303 6.3.3 THE GIBBS SAMPLER 307 II
CONTENTS 6.3.4 RAO-BLACKWELLIZATION 309 6.3.5 THE GENERAL GIBBS SAMPLER
311 6.3.6 THE SLICE SAMPLER 315 6.3.7 THE IMPACT ON BAYESIAN STATISTICS
318 6.4 AN APPLICATION TO MIXTURE ESTIMATION 318 6.5 EXERCISES 321 6.6
NOTES 334 MODEL CHOICE 343 7.1 INTRODUCTION 343 7.1.1 CHOICE BETWEEN
MODELS 344 7.1.2 MODEL CHOICE: MOTIVES AND USES 347 7.2 STANDARD
FRAMEWORK 348 7.2.1 PRIOR MODELING FOR MODEL CHOICE 348 7.2.2 BAYES
FACTORS 350 7.2.3 SCHWARTZ S CRITERION 352 7.2.4 BAYESIAN DEVIANCE 354
7.3 MONTE CARLO AND MCMC COMPUTATIONS 356 7.3.1 IMPORTANCE SAMPLING 356
7.3.2 BRIDGE SAMPLING 358 7.3.3 MCMC METHODS 359 7.3.4 REVERSIBLE JUMP
MCMC , 363 7.4 MODEL AVERAGING 366 7.5 MODEL PROJECTIONS 369 7.6
GOODNESS-OF-FIT 374 7.7 EXERCISES 377 7.8 NOTES 386 ADMISSIBILITY AND
COMPLETE CLASSES 391 8.1 INTRODUCTION 391 8.2 ADMISSIBILITY OF BAYES
ESTIMATORS 391 8.2.1 GENERAL CHARACTERIZATIONS 391 8.2.2 BOUNDARY
CONDITIONS 393 8.2.3 INADMISSIBLE GENERALIZED BAYES ESTIMATORS 395 8.2.4
DIFFERENTIAL REPRESENTATIONS 396 8.2.5 RECURRENCE CONDITIONS 398 8.3
NECESSARY AND SUFFICIENT ADMISSIBILITY CONDITIONS 400 8.3.1 CONTINUOUS
RISKS 401 8.3.2 BLYTH S SUFFICIENT CONDITION 402 8.3.3 STEIN S NECESSARY
AND SUFFICIENT CONDITION 407 8.3.4 ANOTHER LIMIT THEOREM 407 8.4
COMPLETE CLASSES 409 8.5 NECESSARY ADMISSIBILITY CONDITIONS 412 8.6
EXERCISES 416 8.7 NOTES 425 CONTENTS XIX 9 INVARIANCE, HAAR MEASURES,
AND EQUIVARIANT ESTIMATORS 427 9.1 INVARIANCE PRINCIPLES 427 9.2 THE
PARTICULAR CASE OF LOCATION PARAMETERS 429 9.3 INVARIANT DECISION
PROBLEMS 431 9.4 BEST EQUIVARIANT NONINFORMATIVE DISTRIBUTIONS 436 9.5
THE HUNT-STEIN THEOREM 441 9.6 THE ROLE OF INVARIANCE IN BAYESIAN
STATISTICS 445 9.7 EXERCISES 446 9.8 NOTES 454 10 HIERARCHICAL AND
EMPIRICAL BAYES EXTENSIONS 457 10.1 INCOMPLETELY SPECIFIED PRIORS 457
10.2 HIERARCHICAL BAYES ANALYSIS 460 10.2.1 HIERARCHICAL MODELS 460
10.2.2 JUSTIFICATIONS 462 10.2.3 CONDITIONAL DECOMPOSITIONS 465 10.2.4
COMPUTATIONAL ISSUES 468 10.2.5 HIERARCHICAL EXTENSIONS FOR THE NORMAL
MODEL 470 10.3 OPTIMALITY OF HIERARCHICAL BAYES ESTIMATORS 474 10.4 THE
EMPIRICAL BAYES ALTERNATIVE 478 10.4.1 NONPARAMETRIC EMPIRICAL BAYES 479
10.4.2 PARAMETRIC EMPIRICAL BAYES 481 10.5 EMPIRICAL BAYES
JUSTIFICATIONS OF THE STEIN EFFECT 484 10.5.1 POINT ESTIMATION 485
10.5.2 VARIANCE EVALUATION 487 10.5.3 CONFIDENCE REGIONS 488 10.5.4
COMMENTS 490 10.6 EXERCISES 490 10.7 NOTES 502 11 A DEFENSE OF THE
BAYESIAN CHOICE 507 A PROBABILITY DISTRIBUTIONS 519 A.I NORMAL
DISTRIBUTION, AF P (8, E) 519 A.2 GAMMA DISTRIBUTION, Q(A, (3) 519 A.3
BETA DISTRIBUTION, BE(A, /3) 519 A.4 STUDENT S T-DISTRIBUTION, T P {Y,
9, E) 520 A.5 FISHER S F-DISTRIBUTION, T{V, G) 520 A.6 INVERSE GAMMA
DISTRIBUTION, IQ(A,/3) 520 A. 7 NONCENTRAL CHI-SQUARED DISTRIBUTION, XTW
520 A.8 DIRICHLET DISTRIBUTION, T K{A , * * *, A/T) 521 A.9 PARETO
DISTRIBUTION, -L?A(A,XO) 521 A.10 BINOMIAL DISTRIBUTION, B(N,P). 521
A.LL MULTINOMIAL DISTRIBUTION, MK(N;PI,. *. ,PK) 521 A. 12 POISSON
DISTRIBUTION, V{ ) 521 A.13 NEGATIVE BINOMIAL DISTRIBUTION, AFEG(N,P)
522 XX CONTENTS A. 14HYPERGEOMETRIC DISTRIBUTION, HYP(N;N;P) 522 B
USUAL PSEUDO-RANDOM GENERATORS 523 B.I NORMAL DISTRIBUTION, W(0,1) 523
B.2 EXPONENTIAL DISTRIBUTION, XP(X) 523 B.3 STUDENT S T-DISTRIBUTION,
T{V, 0,1) 524 B.4 GAMMA DISTRIBUTION, Q(A, 1) 524 B.5 BINOMIAL
DISTRIBUTION, B(N,P) 525 B.6 POISSON DISTRIBUTION, V(X) 525 C NOTATIONS
527 C.I MATHEMATICAL 527 C.2 PROBABILISTIC . 528 C.3 DISTRIBUTIONAL 528
C.4 DECISIONAL 529 C.5 STATISTICAL 529 C.6 MARKOV CHAINS 530 D
REFERENCES 531 AUTHOR INDEX 581 SUBJECT INDEX 589
|
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| dewey-tens | 510 - Mathematics |
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| edition | 2. ed. |
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| language | English French |
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| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Robert, Christian P. 1961- Verfasser (DE-588)115436448 aut Analyse statistique bayésienne The Bayesian choice from decision-theoretic foundations to computational implementation Christian P. Robert 2. ed. New York [u.a.] Springer 2001 XXII, 604 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Literaturverz. S. 531 - 579 Bayes-Entscheidungstheorie - Lehrbuch Bayes-Verfahren - Lehrbuch CD-ROM (DE-588)4139307-7 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Bayes-Entscheidungstheorie (DE-588)4144220-9 s CD-ROM (DE-588)4139307-7 s 1\p DE-604 Bayes-Verfahren (DE-588)4204326-8 s 2\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009447679&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 | Robert, Christian P. 1961- The Bayesian choice from decision-theoretic foundations to computational implementation Bayes-Entscheidungstheorie - Lehrbuch Bayes-Verfahren - Lehrbuch CD-ROM (DE-588)4139307-7 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4139307-7 (DE-588)4204326-8 (DE-588)4144220-9 (DE-588)4123623-3 |
| title | The Bayesian choice from decision-theoretic foundations to computational implementation |
| title_alt | Analyse statistique bayésienne |
| title_auth | The Bayesian choice from decision-theoretic foundations to computational implementation |
| title_exact_search | The Bayesian choice from decision-theoretic foundations to computational implementation |
| title_full | The Bayesian choice from decision-theoretic foundations to computational implementation Christian P. Robert |
| title_fullStr | The Bayesian choice from decision-theoretic foundations to computational implementation Christian P. Robert |
| title_full_unstemmed | The Bayesian choice from decision-theoretic foundations to computational implementation Christian P. Robert |
| title_short | The Bayesian choice |
| title_sort | the bayesian choice from decision theoretic foundations to computational implementation |
| title_sub | from decision-theoretic foundations to computational implementation |
| topic | Bayes-Entscheidungstheorie - Lehrbuch Bayes-Verfahren - Lehrbuch CD-ROM (DE-588)4139307-7 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayes-Entscheidungstheorie - Lehrbuch Bayes-Verfahren - Lehrbuch CD-ROM Bayes-Verfahren Bayes-Entscheidungstheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009447679&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT robertchristianp analysestatistiquebayesienne AT robertchristianp thebayesianchoicefromdecisiontheoreticfoundationstocomputationalimplementation |