【下载】Bayesian Theory~Jose M. Bernardo, Adrian F. M. Smith.1994-经管之家官网！

ISBN: 978-0-471-92416-6
Hardcover
608 pages
May 1994
Wiley List Price: US $380.00
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This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics
ix
Contents
1. INTRODUCTION
1.1. Thomas Bayes
1.2. The subjectivist view of probability 2
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
2. FOUNDATIONS
13
2.1. Beliefs and actions 13
2.2. Decision problems 16
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
2.5.2. Bounded decision problems
2.5.3. General decision problems
49
50
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
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 165
4.2. Exchangeability and related concepts 167
4.2.1. Dependence and independence 167
4.2.2. Exchangeability and partial exchangeability 168
4.3. Models via exchangeability In
4.3.1. The Bernoulli and binomial models In
4.3.2. The multinomial model 176
4.3.3. The general model 177
Contents
4.4. Models via invariance 181
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 190
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
4.8.1. Representation theorems
4.8.2. Subjectivity and objectivity
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 742
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
xiii
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
6.1.1. Ranges of models 377
6.1.2. Perspectives on model comparison 383
6.1.3. Model comparison as a decision problem 386
6.1.4. Zero-one utilities and Bayes factors 389
6.1.5. General utilities 395
6.1.6. Approximation by cross-validation 403
6.1.7. Covariate selection 407
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.1. Probability distributions 427
A.2. Inferential processes 436
B. NON-BAYESIAN THEORIES 443
B.1. 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