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Berger J.O. — Statistical decision theory and bayesian analysis
Berger J.O. — Statistical decision theory and bayesian analysis



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Название: Statistical decision theory and bayesian analysis

Автор: Berger J.O.

Аннотация:

"The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1985

Количество страниц: 617

Добавлена в каталог: 04.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-Bayes risk      213
$\Gamma$-minimax approach      215 222
$\Gamma$-minimax regret approach      218
$\Gamma$-posterior expected loss      205
$\varepsilon$-minimax strategy      346
Adaptive ridge regression estimators      557
Admissibility      10
Admissibility and complete classes      522
Admissibility and stopping rules      509
Admissibility of Bayes rules      253
Admissibility of generalized Bayes rules      254
Admissibility of invariant rules      422
Admissibility of lower boundary points      336
Admissibility of minimax rules      371
Admissibility of multivariate tests of a point null hypothesis      539
Admissibility of one-sided tests      530
Admissibility of sample mean in 1 or 2 dimensions      548 549
Admissibility of SPRT      498
Admissibility, Stein’s necessary and sufficient condition for      546
Admissibility, verification of      547
Admissibility, verification of, in estimating normal means      552
Admissibility, verification of, in estimating Poisson means      553
Aitchison, J.      67 158 169
Aitkin, M.      26
Akaike, H.      89
Alam, K.      369
Albert, J.H.      169 218
Allais, M.      50
Alpert, M.      82
Alvo, M.      481
Amster, S.J.      457
Anscombe, F.J.      228 503
Antoniak, C.E.      107 183
Armitage, P.      507
Arnold, S.F.      369
Arrow, K.J.      281 444
Asymptotically pointwise optimal      477
Atchison, T.A.      169
Bacharach, M.      281
Bahadur, R.R.      489 506
Balder, E.J.      523 537
Baranchik, A.J.      369
Barlow, R.E.      277 510
Barnard, G.A.      26 31 503
Barndorff-Nielsen, O.      572
Barnett, V.      26 76
Bartholomew, D.J.      503
Basu, D.      31 32 33 503 507
Bayes decision rules      17 159 see
Bayes decision rules, admissibility and inadmissibility of      253
Bayes decision rules, complete class of      337 523
Bayes decision rules, limits of      537 546 547
Bayes decision rules, possible nonexistence of      382
Bayes decision rules, robustness of      see "Robustness"
Bayes decision rules, sequential      444
Bayes factor      146 150 152
Bayes m-inner truncated procedure      460
Bayes m-inner truncated procedure, as approximation to Bayes procedure      461
Bayes m-truncated procedure      449
Bayes m-truncated procedure for sequential sample      451
Bayes m-truncated procedure, as approximation to Bayes procedure      454 455 459 461
Bayes m-truncated procedure, as exact Bayes procedure      454 455
Bayes m-truncated procedure, possible nonexistence of      459
Bayes risk      11 159
Bayes risk of sequential procedures      445
Bayes risk principle      17
Bayes risk with sampling cost      435
Bayes risk, concavity of      483
Bayes, T.      3 89 96 116 129
Bayesian calculation      262
Bayesian calculation in hierarchical problems      192 194 238 242 245 247
Bayesian calculation of credible sets      142
Bayesian calculation, approximations      265
Bayesian calculation, Monte Carlo integration      262
Bayesian calculation, numerical integration      263
Bayesian communication      267 282
Bayesian decision theory      158
Bayesian decision theory with inference losses      166
Bayesian decision theory, choice of sample size      435
Bayesian decision theory, classification problems      165 357
Bayesian decision theory, estimation      161
Bayesian decision theory, extensive form of      160
Bayesian decision theory, finite action problems      163
Bayesian decision theory, hypothesis testing      163
Bayesian decision theory, normal form of      160
Bayesian decision theory, robustness      see "Robustness"
Bayesian expected loss      8 see
Bayesian inference      132
Bayesian inference and classical inference      119 137 406
Bayesian inference, credible sets      140 143
Bayesian inference, decision-theoretic      166
Bayesian inference, estimation      133
Bayesian inference, hypothesis testing      145 268
Bayesian robustness      see "Robustness"
Bayes’s theorem      129
Bechhofer, R.E.      541
Becker, G.M.      53
Berger, J.      15 24 26 27 29 31—33 35 37 66 90 98 99 110 113 120 124 126 148 151—154 156 168 169 178 183 195 197—199 203 205—207 211 215 217 220 221 226—228 233 237 240 242—244 247 258 266 268 361—370 503 506 509 510 542 543 549 550 552 554
Berger, R.      217 278
Berk, R.H.      545
Berkson, J.      22
Berliner, L.M.      98 99 169 178 203 205 207 211 213 215 217 221 233 364 369 554
Bermudez, J.D.      277
Bernardo, J.M.      66 89 90 94 110 231 277
Berry, D.      107 183 435 481
Best invariant decision rule      397 409
Bhattacharya, P.K.      366
Bibby, J.      369
Bickel, P.J.      217 221 222 353 477 479 480
Binomial probability      562
Binomial probability, conjugate prior for      287
Binomial probability, estimators of invariant      394 401
Binomial probability, estimators of minimax      353 375
Binomial probability, estimators of sequential Bayes      454 457
Binomial probability, likelihood function for      28
Binomial probability, noninformative prior for      89
Binomial probability, testing simple hypotheses, minimax      355
Binomial probability, testing simple hypotheses, sequential Bayes      451 456 462
Binomial probability, testing simple hypotheses, SPRT      495 518
Birnbaum, A.      23 31 32 37 503 539
Bishop, Y.      169 183
Blackwell, D.      41 260 327 346 355 379 380 384 422 444
Blum, J.R.      215
Blyth, C.R.      547 548
Bock, M.E.      369
Bondar, J.V.      259 420
Bordley, R.F.      277
Borel, E.      310
Bounded from below      336 355
Box, G.E.P.      35 89 110 119 124 133 183 201 203 249
Boyer, J.E., Jr.      169
Brandwein, A.      361
Brier, G.W.      66
Brockett, P.L.      94 232
Brown, L.D.      26 159 221 251 346 350 360 369 370 423 500 534 535 537 540—543 545—547 549 550 552—554
Brown, P.J.      369
Brown, R.V.      198 277
Bryk, A.S.      169
Buehler, R.J.      259—261 413
Bunke, O.      361
Campbell, F.      364
Caridi, F.      542
Casella, G.      172 353 369
Casti, J.L.      435
Cauchy distribution      560
Cauchy distribution, Bayesian inference      141
Cauchy distribution, location parameter      83
Censoring      30
Chaloner, K.      432
Charnes, A.      94 232
Chen, C.F.      183
Chen, S.Y.      221 361—363 365 367 368
Cheng, P.      361 550
Chernoff, H.      435 481
Chi-square distribution      560
Chi-square distribution, confidence intervals      417
Chi-square distribution, conjugate prior for      287
Chong-Hong, C.      284
Chou, J.P.      361 363 370
Chow, Y.S.      435
Christensen, R.      107 183
Chuang, D.T.      206 251
Classification problems      165 357
Clevenson, M.      360 370
Closed from below      336 355
Cohen, A.      68 500 534 535 540 541 543 545 549
Coherency      120 259
Cole, N.S.      183
Coleman, A.      314
Colonel Blotto problem      15
Combining evidence      272
Combining evidence, decision-theoretic      277
Complete and essentially complete classes      521
Complete and essentially complete classes for estimating normal means      552
Complete and essentially complete classes for estimating Poisson means      553
Complete and essentially complete classes for estimation in the exponential family      541
Complete and essentially complete classes for finite parameter space, Bayes rules      337 523
Complete and essentially complete classes for finite parameter space, lower boundary of the risk set      335 523
Complete and essentially complete classes for finite parameter space, testing simple hypotheses      524
Complete and essentially complete classes for multivariate testing of a point null hypothesis      539
Complete and essentially complete classes for one-sided sequential testing      540
Complete and essentially complete classes for one-sided testing      527 530
Complete and essentially complete classes, admissible rules      522
Complete and essentially complete classes, Bayes rules      337 523 546
Complete and essentially complete classes, decision rules based on a sufficient statistic      36 522
Complete and essentially complete classes, decision rules with continuous risk functions      545
Complete and essentially complete classes, generalized Bayes rules      541 552 553
Complete and essentially complete classes, limits of Bayes rules      537 546 547
Complete and essentially complete classes, monotone decision rules      547
Complete and essentially complete classes, nonrandomized decision rules      40 523 541
Complete and essentially complete classes, two-sided tests      538
Compound decision theory      96 172
Concave function      39 45
Conditional Bayes principle      16
Conditional perspective      24 29 33 44 124 160 214 502 506
Confidence level      414
Confidence principle      23 215
Confidence rules or sets      414 see
Confidence rules or sets, invariant      414 416 417
Confidence rules or sets, lack of final precision      24
Confidence rules or sets, loss functions for      65
Confidence rules or sets, size of      41 415 416
Conjugate prior      see "Prior distribution"
Convex combination      38
Convex function      38 39 45
Convex hull      38
Convex set      38
Copas, J.B.      169
Cornfield, J.      577
Cox, D.R.      23 25
Credible sets      140
Credible sets, coincidence with confidence sets      141 414
Credible sets, highest posterior density (HPD)      140 418
Credible sets, lack of invariance of HPD      144
Credible sets, loss functions for      167
Credible sets, multivariate      143 189
Credible sets, S-optimal      145 291
Credible sets, size of      140 415 430
Cressie, N.      104 169
Dalal, S.R.      132
Das Gupta, A.      151 156 228 247 266 268 361 370 550
Dawid, A.P.      89 106 228
de Finetti, B.      66 75 76 106 119 121 283
De Robertis, L.      197 205 206
de Waal, D.      280 281
Decision rule      9 12
Decision rule, Bayes      17 159
Decision rule, Bayes sequential procedure      444
Decision rule, invariant      395
Decision rule, minimax      18
Decision rule, monotone      532 535
Decision rule, nonrandomized      9
Decision rule, randomized      12
Decision rule, sequential decision procedure      441
Deely, J.J.      183 195 217
DeGroot, M.H.      50 53 71 75 108 148 183 225 278 287 292 435 474
Dempster, A.P.      100 148 153 169 195 203 249 252 277
Density, beta      560
Density, binomial      562 see
Density, Cauchy      560 see
Density, chi-square      560 see
Density, Dirichlet      561
Density, exponential      560 see
Density, exponential family      526 see
Density, F (or Fisher)      560
Density, gamma      560 see
Density, geometric      562 see
Density, inverse gamma      561
Density, multinomial      562 see
Density, multivariate normal      560 see
Density, multivariate t      561
Density, negative binomial      562 see
Density, normal      559 see "Normal
Density, t (or Student’s t)      561 see
Density, uniform      560 see
Dey, D.K.      243 244 361 369
Diaconis, P.      106 132 159 229 277 283 346 361 537 546
Diamond, G.A.      120 151
Dickey, J.M.      76 96 148 151 152 183 206 228 246 267 268 277 284
Donovan, T.M.      217
DuMouchel, W.M.      183
Dunsmore, I.R.      67 158
Dutch book arguments      259
Dvoretsky, A.      523
Eaton, M.L.      66 261 391 539
Eberl, W.Jr.      580
Eddy, W.F.      203 249
Edwards, A.W.F.      26 31
Edwards, W.      81 119 124 152 153 223 503 504
Efron, B.      169 178 219 221 244 361 365 369
Ellsberg, D.      122
Empirical Bayes methods      96 167
Empirical Bayes methods for exchangeable normal means      169
Empirical Bayes methods for general normal means      173
Empirical Bayes methods for Poisson means      178
Empirical Bayes methods, construction of prior      96 167
Empirical Bayes methods, nonparametric empirical Bayes (NPEB)      168 178
Empirical Bayes methods, parametric empirical Bayes (PEB)      168 169 173
Empirical Bayes methods, use of monotonization      536
entropy      66 91 92 104
Equalizer decision rule      353
Equalizer strategy      322 325 337 379
Essentially complete classes      521 see
Estimation      5 9
Estimation, Bayes      133 161
Estimation, Bayes for absolute error loss      162
Estimation, Bayes for linear loss      162
Estimation, Bayes for quadratic loss      293
Estimation, Bayes for squared-error loss      161
Estimation, Bayes in inference      133
Estimation, Bayes, error      136
Estimation, Bayes, robustness of      see "Robustness"
Estimation, best invariant      405
Estimation, best invariant for location parameter      398 399 405 427
Estimation, best invariant for scale parameter      400 428
Estimation, empirical Bayes      167
Estimation, empirical Bayes for normal means      169 173
Estimation, empirical Bayes for Poisson means      178
Estimation, hierarchical Bayes      180
Estimation, minimax      350 353 363 369
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