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Bernardo J.M., Smith A.F.M. — Bayesian Theory
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Название: Bayesian Theory
Авторы: Bernardo J.M., Smith A.F.M.
Аннотация: 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 authorss 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.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2000
Количество страниц: 586
Добавлена в каталог: 12.04.2010
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Предметный указатель
A posteriori distribution see "Posterior distribution"
A priori distribution see "Prior distribution"
Abramowitz, M. 156 489
Absolutely continuous distribution, multivariate 128 434 435
Absolutely continuous distribution, univariate 111 430—433
Absolutely continuous random quantity 109—111
Achcar, J.A. 345 489
Actions 5 13 15—17
Actions in bounded decision problems x 50—54
Actions in general decision problems x 54—56
Actions set of x 16 19—21
Actuarial science 9 100 373
Aczel, J. 91 489
Additive decomposition of utility 66 149 408
Adekola, A.D. 289 548
Admissibility 447—449 461
Admissibility and complete classes 448
Admissibility of Bayes rules 448 449
Admissible decision see "Admissibility"
Aitchison, J. 10 99 262 483 489
Aitken, C.G.G. 10 489
Aitkin, M. 417 489
Akaike information criterion 487 488
Akaike, H. 359 367 455 487 489 490
Albert, J.H. 352 426 481 490
Aldous, D. 236 490
Allais, M. 96 97 98 490
Amaral-Turkman, M.A. 483 490
Ameen, J.R.M. 374 490
Amount of information 6 77—81 157—159 303 422
Amster, S.J. 376 490
Analysis of variance 382
Ancillarity xii 7 452 453 475 479
Andersen, E.B. 455 481 490
Anderson, T.W. 376 445 490
Angers, J.-F. 371 490
Anscombe, F.J. 10 85 295 490
Ansley, C.F. 374 491
Antoniak, C. 228 491
Aoki, M. 10 374 491
Approximations and discrepancy x xi 75—77 154—157 207—209
Approximations of a Binomial by a Poisson 76 77
Approximations of a Student by a Normal 156
Approximations of moments of a transformed beta distribution 124 125
Approximations of prior distributions 283—285
Approximations of the mean of a beta distribution 344 345
Approximations to mean and variance 113
Approximations to mean vector and covariance 132
Approximations, asymptotic see "Asymptotic analysis"
Approximations, Gibbs sampling algorithm 353—355
Approximations, importance sampling xiii 8 264 340 348—350
Approximations, iterative quadrature xiii 264 346—348
Approximations, Laplace approximation xiii 8 264 340—345 455
Approximations, Markov chain Monte Carlo xiii 8 264 340 353—356
Approximations, Metropolis — Hastings algorithm 355 356
Approximations, sampling-importance-resampling xiii 8 264 340 350—352
Arimoto, S. 91 491
Arnaiz, G. 230 491
Arnold, S.F. 11 491
Arrow, K.J. 91 103 104 491
Ascending factorial function 135
Ash, R.B. 106 111 162 173 491
Asymptotic analysis xiii 8 235 264 285—297 445 463—465 480 485 486 see
Asymptotic analysis, continuous xiii 287—297
Asymptotic analysis, discrete xiii 286 287
Asymptotic analysis, non-normal 296
Asymptotic normality for a ratio 297
Asymptotic normality of posterior distributions 286—297 314 365
Asymptotic normality, regularity conditions for 289—292
Asymptotic normality, under conjugate analysis 293 294
Asymptotic normality, under transformations xiii 295—297 486
Aumann, R.J. 85 104 490 491
Axiomatic approaches 5 83—91
Axiomatic approaches to degrees of belief 89 90
Axiomatic approaches to utilities 90 91
Axiomatic approaches, relevance of 94 95 see
Axioms of coherence 15 16 23—28
Aykac, A. 10 491
Backward induction x 59—63
Bahadur, R.R. 451 491
Bailey, R.W. 123 491
Balch, M. 85 491
Bandemer, H. 160 491
Barlow, R.E. 11 104 172 236 374 491 492 523
Barnard, G.A. 2 95 250 270 362 376 455 458 492
Barndorff-Nielsen, O.E. 206 455 481 484 492
Barnett, V. 102 376 445 492
Barrai, I. 10 492
Bartholomew, D.J. 11 376 492
Bartlett, M. 422 493
Basu, D. 136 250 374 376 452 453 468 479 481 493
Bauwens, L. 10 493
Bayarri, M.J. viii 104 243 250 313 338 364 371 417 418 493 494 496
Bayes decision rule 448
Bayes estimate see "Estimation"
Bayes factor xiii 389—395 414 417 422—424 470 476 487 488
Bayes risk 448
Bayes rules 448
Bayes test 391—397 412—417
Bayes — Laplace postulate 357 358
Bayes' theorem xii 2 4 7 162 175 180 241—255 265 269—285 305 306 340 352 368 425 451 452 454 455 480
Bayes' theorem generalised xi xiii 127 130
Bayes' theorem, finite x 2 38—40 42—45 47—49 68 77 80 89 94
Bayes, T. 1 2 89 101 102 356 357 482 494
Bayes, Thomas 1 2
Bayesian bootstrap 371
Bayesian computation vii 5
Bayesian implementation 8 263—356
Bayesian inference see "Inference Bayesian"
Bayesian methods vii 5
Bayesian paradigm xiii 241—264
Bayesian reading list ix 9—11
Bayesian software 425 426
Bayesian theory vii ix 5—9
Beauchamp, T.J. 232 534
Becker, G.M. 91 494
Belief functions 95 99
Beliefs 3—9 13—16 33—49
Beliefs and actions x 13—16
Beliefs and limiting frequencies 173—175 177 179 181
Beliefs and models xi xiii 165—167
Beliefs and probabilities x 33—49
Beliefs, conditional x 38—49
Beliefs, finite representation of x 33—38
Beliefs, general representation of xi 105—109
Beliefs, reporting of x xi 67—81 150—157 302 320 360
Beliefs, revision of x 38—49 127—130
Beliefs, sequential revision of x 47—49 56—67
Bellman, R.E. 61 494
Berger, J.O. viii 9 10 11 102 250 258 263 302 306 307 333 334 337 338 362 366 370 371 373 375 394 417 423 449 475 479 490 493 494 495 496 506 519 520 536 554
Berger, R.L. 104 376 445 475 495 500
Berk, R.H. 287 495
Berliner, L.M. 228 371 374 494 495 496
Bermudez, J.D. 71 232 289 419 496 497
Bernardo, J.M. 9 10 11 18 71 92 141 156 232 302 305 306 307 313 323 333 334 337 338 362 365 366 373 374 394 417 419 422 468 481 483 494 495 496 497
Bernoulli distribution and exchangeability xi 172—175 211—215
Bernoulli distribution, "biased" stopping rule for 251 252
Bernoulli distribution, asymptotic analysis for 294 296
Bernoulli distribution, conjugate analysis of 270—272 436
Bernoulli distribution, conjugate family for 267 270
Bernoulli distribution, inferential process for 248 249 270—274 276 277 279—282 436
Bernoulli distribution, model 115 428
Bernoulli distribution, reference distributions for 315 316 337 436
Bernoulli distribution, sufficient statistics for 195 196 436
Bernoulli, D. 87 497
Bernoulli, J. 89 101 497
Berry, D.A. 10 160 376 495 497 536
Besag, J. 353 356 374 497
Bessant, R.G. 44 535
Best, N.G. 353 355 516
Beta distribution 116 117 124 125 134 135 430
Beta distribution as prior distribution 267 270—273 344
Beta distribution, mixtures of 279—281
Beta-binomial distribution see "Binomial-beta distribution"
Betting see "Monetary Bets"
Bias 360 462—465
Bickel, P.J. 455 463 497
Bilateral Pareto distribution 141 434
Binder, S. 373 497
Binomial distribution see also "Bernoulli distribution"
Binomial distribution, asymptotic analysis for 294 296
Binomial distribution, conjugate analysis of 270—272
Binomial distribution, conjugate family for 267 271
Binomial distribution, inferential process for 248 249 270—274 279—282 414
Binomial distribution, model 115 134 172—175 211—215 428
Binomial distribution, reference distributions for 315 316 337
Binomial distribution, sufficient statistics for 195 196
Binomial-beta distribution 117 272 428
Bioassay 219 220 382
Biostatistics 9
Birnbaum, A. 11 250 455 456 497
Bjornstad, J.F. 455 485 498
Blackwell, D. 91 103 159 356 463 464 498
Blyth, C.R. 42 498
Boos, D.D. 455 534
Booth, N.B. 374 498
Bootstrap 371 see bootstrap"
Bordley, R.F. 96 498
Borel, E. 89 498
Borelset 110 127
Borovcnik, M. 9 498
Bowen, K.C. 10 104 552
Box, G.E.P. 9 10 44 92 93 230 231 258 260 263 360 361 367 370 376 413 417 419 498 499 549
Boyer, J.E.Jr. 373 516
Boyer, M. 10 499
Brant, R. 418 500
Breslow, N. 11 499
Bretthorst, G.L. 10 499
Bridgman, P.W. 82 499
Brier, G.W. 71 499
Brillinger, D.R. 458 499
Broemeling, L.D. 10 499
Brown, L.D. 10 206 258 499
Brown, P.J. 10 373 374 499
Brown, R.V. 100 104 499 531
Brown, S.J. 420 527
Brumat, C. 10 491
Brunk, H.D. 162 499
Buehler, R.J. 88 154 468 469 499
Bunn,D.J. 104 499
Butler, R.W. 455 485 499
Calibration 373 482
Called-off bets 87—89
Campling, G.E.G. 374 552
Cano, J.A. 371 394 451 500 534
Canonical conjugate analysis 269—279
Carlin, B.P. 355 374 500
Carlin, J.B. 371 500
Carnap, R. 90 100 500
Caro, E. 104 500
Casella, G. 353 376 445 468 469 475 500 519 532
Cauchy distribution 123 349
Cauchy distribution, location parameter estimation 451
Central limit theorem 126
Centred spherical symmetry 183—186
Chaloner, K. 160 418 500
Chan, K.S. 353 500
Chang, H. 418 419 420 515
Chang, T. 362 500
Chankong, V. 104 500
Chao, M.T. 289 500
Characteristic function 114 126 183—186 203
Chateaneuf, A. 99 500
Chen, C.F. 289 501
Chernoff, H. 10 91 160 475 501
Chi-squared distribution 118 121 123 124 138 330 361 414 431 459 487
Choice of experiments see "Design of experiments"
Chow, Y.S. 178 501
Christ, D.E. 261 523
Chuang, D.T. 371 525
Chuaqui, R. 90 501
Cifarelli, D.M. 9 10 11 483 501
Clarke, B. 367 501
Clarke, R.D. 100 501
Claroti, C.A. 10 501
Classical decision theory xiv 444—449 461
Classification 373 407 408 483
Clayton, D.G. 353 355 516
Clayton, M.K. 104 419 501 516
Clemen, R.T. 104 501
Closed under sampling 270 281 see
Cluster analysis 418
Cochrane, J.L. 104 501
Coding theory 358 see
Coherence x 23—33 38—45 83—91 94—99 195 see
Coherence and preferences x 23—28
Coherence and quantification x 28—33 83—85
Coherence, temporal 94
Coletti,G. 10 492
Collier, R.O. 10 412
Combining evidence 103—104
Communication 92 102—104 166 236 237
Comparability of consequences 23 24
Comparability of events 33
Comparative inference xiv 376 443—488
Compatibility of probability and degrees of belief 35 40
Complete probability measures 108
Complete symmetry 169
Composite hypothesis see "Hypothesis"
Computer software 425 426
Conditional, beliefs see "Beliefs"
Conditional, density function 128—131 166 172—226 242—247 353—355
Conditional, expectation 51 52
Conditional, independence see "Independence"
Conditional, inference xiv 374 445 452 468 475 478 479
Conditional, likelihood 48
Conditional, mass function 128—130
Conditional, preference 22 85
Conditional, probability 38—49
Conditional, uncertainty relation 22 38—40
Confidence interval, region 359 445 453 465—469 478 see
Confidence level, coefficient 466
Confirmation theory 95
Conjugate analysis xiii 8 9 264—285 see
Conjugate prior family of distributions, approximation with 279—285
Conjugate prior family of distributions, canonical form of 269
Conjugate prior family of distributions, convex combination (mixtures) of 282 283
Conjugate prior family of distributions, definition of 265 266
Conjugate prior family of distributions, for regular exponential models 266—279
Conjugate prior family of distributions, limiting form of 276 362
Conjugate prior family of distributions, logarithmic divergence between 278
Conlisk, J. 87 501
Consequences 16 17 19—21
Consequences, bounded set of 49—54
Consequences, extreme 49—54
Consequences, reference 54—56
Consistency of preferences 26
Consistent sequence of statistics, estimates 312 320 326 353 405
Consonni, G. 279 422 501
Constrained parameters 246 247
Contingency table 41 216 374 414
Continuity of uncertainty relation 107
Control problems, theory 9 374
Convergence xi 125—127
Convergence in distribution 125 126
Convergence in expected utility 142—147
Convergence in mean square 125 126
Convergence in probability 125 126
Convergence, almost surely 125 126 352
Cook, R.D. 418 551
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