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Berger J.O. — Statistical decision theory and bayesian analysis
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Название: Statistical decision theory and bayesian analysisАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2nd editionГод издания: 1985Количество страниц: 617Добавлена в каталог: 04.12.2005Операции: Положить на полку |
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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, 215 222 Robustness of Bayes rules, 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 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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