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Bernardo J.M., Smith A.F.M. Ч Bayesian Theory
Bernardo J.M., Smith A.F.M. Ч Bayesian Theory

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Ќазвание: Bayesian Theory

јвторы: Bernardo J.M., Smith A.F.M.

јннотаци€:

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 Сprior 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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2000

 оличество страниц: 586

ƒобавлена в каталог: 12.04.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный 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 430Ч433
Absolutely continuous random quantity      109Ч111
Achcar, J.A.      345 489
Actions      5 13 15Ч17
Actions in bounded decision problems      x 50Ч54
Actions in general decision problems      x 54Ч56
Actions set of      x 16 19Ч21
Actuarial science      9 100 373
Aczel, J.      91 489
Additive decomposition of utility      66 149 408
Adekola, A.D.      289 548
Admissibility      447Ч449 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 77Ч81 157Ч159 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 75Ч77 154Ч157 207Ч209
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      283Ч285
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      353Ч355
Approximations, importance sampling      xiii 8 264 340 348Ч350
Approximations, iterative quadrature      xiii 264 346Ч348
Approximations, Laplace approximation      xiii 8 264 340Ч345 455
Approximations, Markov chain Monte Carlo      xiii 8 264 340 353Ч356
Approximations, Metropolis Ч Hastings algorithm      355 356
Approximations, sampling-importance-resampling      xiii 8 264 340 350Ч352
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 285Ч297 445 463Ч465 480 485 486 see
Asymptotic analysis, continuous      xiii 287Ч297
Asymptotic analysis, discrete      xiii 286 287
Asymptotic analysis, non-normal      296
Asymptotic normality for a ratio      297
Asymptotic normality of posterior distributions      286Ч297 314 365
Asymptotic normality, regularity conditions for      289Ч292
Asymptotic normality, under conjugate analysis      293 294
Asymptotic normality, under transformations      xiii 295Ч297 486
Aumann, R.J.      85 104 490 491
Axiomatic approaches      5 83Ч91
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 23Ч28
Aykac, A.      10 491
Backward induction      x 59Ч63
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 389Ч395 414 417 422Ч424 470 476 487 488
Bayes risk      448
Bayes rules      448
Bayes test      391Ч397 412Ч417
Bayes Ч Laplace postulate      357 358
Bayes' theorem      xii 2 4 7 162 175 180 241Ч255 265 269Ч285 305 306 340 352 368 425 451 452 454 455 480
Bayes' theorem generalised      xi xiii 127 130
Bayes' theorem, finite      x 2 38Ч40 42Ч45 47Ч49 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 263Ч356
Bayesian inference      see "Inference Bayesian"
Bayesian methods      vii 5
Bayesian paradigm      xiii 241Ч264
Bayesian reading list      ix 9Ч11
Bayesian software      425 426
Bayesian theory      vii ix 5Ч9
Beauchamp, T.J.      232 534
Becker, G.M.      91 494
Belief functions      95 99
Beliefs      3Ч9 13Ч16 33Ч49
Beliefs and actions      x 13Ч16
Beliefs and limiting frequencies      173Ч175 177 179 181
Beliefs and models      xi xiii 165Ч167
Beliefs and probabilities      x 33Ч49
Beliefs, conditional      x 38Ч49
Beliefs, finite representation of      x 33Ч38
Beliefs, general representation of      xi 105Ч109
Beliefs, reporting of      x xi 67Ч81 150Ч157 302 320 360
Beliefs, revision of      x 38Ч49 127Ч130
Beliefs, sequential revision of      x 47Ч49 56Ч67
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 172Ч175 211Ч215
Bernoulli distribution, "biased" stopping rule for      251 252
Bernoulli distribution, asymptotic analysis for      294 296
Bernoulli distribution, conjugate analysis of      270Ч272 436
Bernoulli distribution, conjugate family for      267 270
Bernoulli distribution, inferential process for      248 249 270Ч274 276 277 279Ч282 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 270Ч273 344
Beta distribution, mixtures of      279Ч281
Beta-binomial distribution      see "Binomial-beta distribution"
Betting      see "Monetary Bets"
Bias      360 462Ч465
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      270Ч272
Binomial distribution, conjugate family for      267 271
Binomial distribution, inferential process for      248 249 270Ч274 279Ч282 414
Binomial distribution, model      115 134 172Ч175 211Ч215 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      87Ч89
Campling, G.E.G.      374 552
Cano, J.A.      371 394 451 500 534
Canonical conjugate analysis      269Ч279
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      183Ч186
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 183Ч186 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 444Ч449 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 23Ч33 38Ч45 83Ч91 94Ч99 195 see
Coherence and preferences      x 23Ч28
Coherence and quantification      x 28Ч33 83Ч85
Coherence, temporal      94
Coletti,G.      10 492
Collier, R.O.      10 412
Combining evidence      103Ч104
Communication      92 102Ч104 166 236 237
Comparability of consequences      23 24
Comparability of events      33
Comparative inference      xiv 376 443Ч488
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      128Ч131 166 172Ч226 242Ч247 353Ч355
Conditional, expectation      51 52
Conditional, independence      see "Independence"
Conditional, inference      xiv 374 445 452 468 475 478 479
Conditional, likelihood      48
Conditional, mass function      128Ч130
Conditional, preference      22 85
Conditional, probability      38Ч49
Conditional, uncertainty relation      22 38Ч40
Confidence interval, region      359 445 453 465Ч469 478 see
Confidence level, coefficient      466
Confirmation theory      95
Conjugate analysis      xiii 8 9 264Ч285 see
Conjugate prior family of distributions, approximation with      279Ч285
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      266Ч279
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 19Ч21
Consequences, bounded set of      49Ч54
Consequences, extreme      49Ч54
Consequences, reference      54Ч56
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 125Ч127
Convergence in distribution      125 126
Convergence in expected utility      142Ч147
Convergence in mean square      125 126
Convergence in probability      125 126
Convergence, almost surely      125 126 352
Cook, R.D.      418 551
1 2 3 4 5 6
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