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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
Right invariant Haar densities      406 409 425 429 430
Rios, S.      199
Risk functions      9 13 23 34
Risk functions continuous      254 544
Risk functions of sequential procedures      442
Risk functions, use in Bayesian robustness      218
Risk point      331
Risk set      331
Robbins, H.      96 168 169 178 215 435
Roberts, H.V.      158 510
Robinson, G.K.      66 259—261
Robustness      69
Robustness and ignoring data      251
Robustness of Bayes rules      195 285
Robustness of Bayes rules, $\Gamma$-minimax analysis      215 222
Robustness of Bayes rules, $\Gamma$-minimax regret      218
Robustness of Bayes rules, in estimation      208 226
Robustness of Bayes rules, in testing      211 226
Robustness of Bayes rules, posterior measures      205
Robustness of Bayes rules, risk measures      213 218
Robustness of Bayes rules, use of minimaxity      378
Robustness of Bayes rules, with $\varepsilon$-contamination class      206
Robustness of conjugate priors      195 228
Robustness of empirical Bayes estimators      167
Robustness of hierarchical priors      231
Robustness of losses      61 250
Robustness of maximum entropy priors      94
Robustness of ML-II priors      232
Robustness of models      248
Robustness of noninformative priors      229
Robustness of priors      34 111 195 236
Robustness of priors for determining sample size      441
Robustness of priors, stable estimation      223
Robustness, use of the marginal for      199 248
Rosenblatt, J.      215
Rosenkrantz, R.D.      86 91
Roth, A.J.      100 169
Rubin, D.B.      100 124 169 203 215 510
Rubin, H.      21 50 69 121 195 227 228 260 265 374 460 530 532 533 535
Rubinstein, R.Y.      265
Rukhin, A.L.      206 361 549
Rummel, F.      217
S-games      331 338
Sackrowitz, H.D.      68
Sacks, J.      477 481 542
Sahlin, N.E.      199
Saleh, A.K.Md.E.      361
Sampson, P.F.      100
Samuel-Cahn, E.      500 541
Santner, T.      543
Savage, L.J.      2 26 76 112 119 121 124 152 153 223 281 377 503 504 507
Scale parameters      85 400
Schacter, R.D.      277
Schervish, M.J.      277
Schlaifer, R.      130 151 160 510
Schnieper, R.      169
Schwarz, G.      481
Scissors-Paper-Stone      380
Sclove, S.L.      369
Scoring rules      66
Sedransk, N.      183
Seidenberg, A.      286
Selliah, J.B.      361
Sellke, T.      148 152—154 156 233
Selwyn, M.R.      100 169
Sen, P.K.      361
Sensitivity analysis      196 247
Separating hyperplane      339
Separating hyperplane theorem      339
Sequential analysis      433 441
Sequential analysis, Bayesian      442
Sequential analysis, Bayesian, decision rules      446
Sequential analysis, Bayesian, existence of Bayes procedure      469 472 473
Sequential analysis, Bayesian, procedures for constant posterior risk      447
Sequential analysis, finding and approximating Bayes procedures      448
Sequential analysis, finding and approximating Bayes procedures, accuracy of approximations      462
Sequential analysis, finding and approximating Bayes procedures, asymptotically pointwise optimal      477
Sequential analysis, finding and approximating Bayes procedures, inner truncation      459
Sequential analysis, finding and approximating Bayes procedures, look ahead procedures      455
Sequential analysis, finding and approximating Bayes procedures, solving the functional equation      474 482
Sequential analysis, finding and approximating Bayes procedures, truncated procedures      448
Sequential analysis, loss function for      433 434 511
Sequential analysis, minimax procedures      501
Sequential analysis, stopping rule principle      502
Sequential analysis, testing simple hypotheses      481
Sequential batch sampling      512
Sequential decision procedures      441
Sequential decision procedures, Bayes      445
Sequential decision procedures, existence of      469
Sequential decision procedures, minimax      501
Sequential decision procedures, proper      442
Sequential probability ratio test (SPRT)      481 485 486
Sequential probability ratio test (SPRT), admissibility of      498
Sequential probability ratio test (SPRT), as a Bayes procedure      482 499
Sequential probability ratio test (SPRT), generalized SPRT      540
Sequential probability ratio test (SPRT), one-sided testing      500
Sequential probability ratio test (SPRT), Wald approximations      485
Sequential probability ratio test (SPRT), Wald approximations, accuracy of      495
Sequential sample      433
Shafer, G.      50 59 76 148 156 277 285 286
Shapiro, C.      481
Shigemasu, K.      183
Shinozaki, N.      251 361 369
Shor, S.W.W.      510
Shubik, M.      314
Siegmund, D.      435 500
Significance testing      see "Hypothesis testing"
Simon, G.      265
Singpurwalla, N.D.      136 177 277
Sinha, B.K.      225 550
Siow, A.      148 151 153
Slovic, P.      76 82 106 198
Smiriga, N.G.      277
Smith, A.F.M.      106 122 124 156 183 186 249 262 268
Smith, C.A.B.      121 151 199
Smith, G.      364
Smith, W.S.      76 96
Sobel, M.      540 541
Solomon, D.L.      594
Spiegelhalter, D.J.      156 277
Spruill, M.C.      550
Srinivasan, C.      361 542 543 550 553 554
St.Petersburg paradox      57 71
Stable estimation (or stable measurement)      223
Steele, J.M.      594
Stein phenomenon      360
Stein, C.      66 87 159 230 244 256 346 360 361 363 364 369 413 418 420 422 487 537 543 546 547 549 552
Stein, M.L.      264
Stein’s necessary and sufficient condition for admissibility      546
Stewart, L.      265
Stigler, S.      96 116
Stijnen, Th.      169 534 537
Stone, M.      89 90 260
Stopping rule principle      502
Stopping rule principle and admissibility      509
Stopping rule principle, criticisms of      506
Stopping rules      441
Stopping rules, evidential relevance of      502
Stopping rules, informative      510
Stopping time      442
strategies      310
Strawderman, W.E.      221 237 240 353 361 369 534 535 540 541 543
Strenio, J.F.      169
Strictly determined game      318
Student’s t-distribution      see "t-distribution"
Subjective probability      74 198
Sudderth, W.D.      121 258 259
Sufficient partition      36
Sufficient statistics      35
Sufficient statistics and convex loss      41
Sufficient statistics and posterior distributions      127
Sufficient statistics in sequential analysis      506
Sufficient statistics, complete class      36 422
Supporting hyperplane      339
Supporting hyperplane theorem      339
Susarla, V.      169
t-distribution      561
t-distribution as location density      83
t-distribution as scale density      88
Table entry problem      86
Takada, Y.      369
Tan, W.Y.      183
Test functions      355
Thayer, D.T.      183
Thisted, R.A.      369
Thomas, L.C.      310 314
Tiao, G.C.      35 89 110 119 133 183 203 228 246 249
Tierney, L.      266
Tjur, T.      595
Toutenburg, H.      369
Transitive group      397 405
Truax, d.r.      539
Truncated procedures      see "m-truncated procedures"
Tsao, H.J.      169
Tsui, K.W.      361 363 370
Tversky, A.      76 82 106 198 277
Type I and Type II errors      see "Hypothesis testing" "Error
Type II maximum likelihood      99
Ullah, A.      369
Unbiased estimator of risk      361
Unbiased estimator of risk for normal means      362 386
Unbiased estimator of risk for Poisson means      363 386
Uniform distribution      560
Uniform distribution, credible sets for      290
Uniform distribution, invariant estimation      428
Uniform distribution, sequential Bayes      474 516 520
Uniformly most powerful      326
Utility      47
Utility functions      47
Utility functions and loss functions      57
Utility functions for money      53
Utility functions in game theory and minimax analysis      313 314 376
Utility functions in sequential analysis      433
Utility functions, construction of      48 53
Utility functions, construction of, axioms for      49
Utility functions, multidimensional      53
Value (of a game)      318
van der Merwe, A.J.      182
van der Merwe, C.A.      182
van Dijk, H.K.      265
van Houwelingen, J.C.      534 535 537
van Zyl, G.      280 281
Vardeman, S.      549
Vardi, Y.      481
Velleman, P.      265
Verbeek, A.      535
Villegas, C.      83 89
Vinod, H.D.      369
von Neumann, J.      310
Wagner, C.      281
Wald approximations (for an SPRT)      492
Wald approximations (for an SPRT), accuracy of      495
Wald, A.      2 434 435 444 474 481 486 488 492 498 499 523 537
Walker, A.M.      225
Wallace, D.L.      259
Waller, R.A.      169 215
Wardrop, R.      481
Weak conditionality principle      31
Weerahandi, S.      280 281
Weisberg, H.I.      169
Weiss, L.      597
Whitney, A.W.      168
Whittle, P.      435
Widder, D.V.      544
Williams, J.D.      15 330
Winkler, R.L.      76 96 113 277 281
Winsten, C.B.      503
Wolfenson, M.      199
Wolfowitz, J.      499 523
Wolpert, R.      15 26 29 31 32 33 35 110 120 124 126 369 503 506 509 510
Woodroofe, M.      183 481
Yahav, J.A.      477 479 480
Ylvisaker, D.      132 229
Zabell, S.      277 283
Zacks, S.      597
Zaman, A.      542 554
Zeckhauser, R.      281
Zellner, A.      35 89 90 94 110 133 148 151 153 183 228 246
Zeytinoglu, M.      353
Zheng, Z.      369
Zidek, J.V.      89 277 280 281 360 361 369 370 413 423 550 552
Zimmer, W.J.      217
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