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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:

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

Предметный указатель

Likelihood principle, violated by risk functions      30
Likelihood ratio      146 153 484
Limited translation estimators      219
Lin, P.E.      369
Lindley, D.V.      28 66 75 106 119 121 148 151 156 183 186 195 198 266 275 277 283 286 503
Lindman, H.      119 124 152 153 223 503 504
Lindsay, B.G.      101 178
Linear opinion pool      273
Location parameters      83 497
Location-scale parameters      88 401
Lord, F.M.      104 169
Lorden, G.      481
Loss functions      3
Loss functions for inference problems      64 166 261
Loss functions for randomized rules      13
Loss functions from utility functions      57
Loss functions in sequential analysis      433 434 511
Loss functions, "0—1 and ""      63
Loss functions, absolute error      63
Loss functions, invariant      393
Loss functions, linear      62
Loss functions, m-inner truncated      460
Loss functions, matrix      7 325
Loss functions, quadratic      62
Loss functions, regret      60 377
Loss functions, robustness of      61 250
Loss functions, squared-error      60
Loss functions, vector valued      68
Louis, T.A.      100 177
Lower boundary point      335
Lower quantant      333
Luce, R.D.      281
Lush, J.L.      168
m-inner truncated Bayes risk      460 461 468 469
m-inner truncated loss      460
m-step inner look ahead procedure      461
m-step look ahead procedure      455 456 459 461
m-truncated Bayes risk      448 449 451 461 467
m-truncated procedures      449
Mackay, J.      251
Magwire, C.A.      469
Mandelbaum, a.      550
Marazzi, A.      217 221 222
Marden, J.I.      539
Marginal density      95 128 130 199
Marginal density in empirical Bayes theory      96 169 173
Marginal density in robustness studies      199
Marginal density in sequential analysis      445 450
Marginal density, as likelihood function      99 177 200
Marginal density, as likelihood function, relative likelihoods      201
Marginal density, exchangeability of      104
Marginal density, information about      95
Marginal density, moments of      101
Marginal density, type II maximum likelihood      99 174 223
Maritz, J.S.      104 169
Marschak, J.      53
Martz, H.F.      169 215
Matheson, J.E.      277
Matthes, T.K.      539
McConway, K.J.      277
Meeden, G.      228 543 549 550
Meinhold, R.J.      177
Menges, G.      215
Mensing, R.W.      277
Miescke, K.J.      541
Milnes, P.      420
Minimax analysis      308
Minimax analysis, comparison with Bayesian analysis      373 379
Minimax analysis, conservatism      308 376
Minimax analysis, finite parameter space      354
Minimax analysis, finite parameter space, classification problems      357
Minimax analysis, finite parameter space, testing simple hypotheses      355
Minimax analysis, game theory      310
Minimax analysis, least favorable prior distribution      350 352
Minimax analysis, regret      376 387
Minimax analysis, sequential      501
Minimax analysis, statistical games      347
Minimax analysis, techniques of solution      349
Minimax analysis, techniques of solution, direct method      349
Minimax analysis, techniques of solution, guessing a least favorable prior      350
Minimax analysis, techniques of solution, guessing an equalizer rule      353
Minimax analysis, techniques of solution, using invariance      418
Minimax decision rules      18 see
Minimax decision rules, admissibility and inadmissibility of      371
Minimax decision rules, classes of      359 363 369
Minimax decision rules, sequential      501
Minimax principle      18
Minimax regret      377 387
Minimax strategy      317
Minimax theorem      345
Mintz, M.      353
ML-II estimation      see "Type II maximum likelihood"
Models and exchangeability      106
Models and objectivity      110
Models, compromising between      176
Models, robustness of      248
Models, separation from prior      283
Moeschlin, O.      580
Monotone decision problems      530
Monotone decision problems, estimation      534
Monotone decision problems, multiple decision      530
Monotone decision rules      532 535
Monotone likelihood ratio      357 500 526
Monotone likelihood ratio and uniformly most powerful tests      524
Monotonization of a decision rule      533 535 536
Morgenstern, O.      310
Morris, C.      168—170 172 174 175 178 183 189 194 195 215 219 221 244 361 365 369
Morris, P.A.      277
Moses, L.E.      577
Mousa, A.      369
Muirhead, R.J.      361
Multinomial distribution      562
Multinomial distribution, conjugate prior for      287
Multiple decision problems      see "Finite action problems"
Multivariate normal mean      560
Multivariate normal mean, as location vector      83
Multivariate normal mean, Bayesian analysis with normal prior      139
Multivariate normal mean, Bayesian analysis with normal prior, HPD credible set      143
Multivariate normal mean, conjugate prior for      288
Multivariate normal mean, empirical Bayes estimation      169 173 386
Multivariate normal mean, gamma minimax estimation      222
Multivariate normal mean, generalized Bayes estimators      543
Multivariate normal mean, generalized Bayes estimators, admissibility and inadmissibility      552
Multivariate normal mean, hierarchical Bayes estimation      183 190 386
Multivariate normal mean, inadmissibility of sample mean in 3+ dimensions      256 360 552
Multivariate normal mean, minimax estimators with Bayesian input      220 365 366 368 386
Multivariate normal mean, minimax estimators, class of      363
Multivariate normal mean, minimax estimators, conflict with Bayes      367
Multivariate normal mean, minimax estimators, sample mean      383
Multivariate normal mean, restricted risk Bayes estimation      220
Multivariate normal mean, robust Bayesian analysis of      236
Multivariate normal mean, robust Bayesian analysis of, credible regions      239 242
Multivariate normal mean, robust Bayesian analysis of, estimation      238 242
Multivariate normal mean, robust Bayesian analysis of, for independent coordinates      243
Multivariate normal mean, robust Bayesian analysis of, robust priors      236 242
Multivariate normal mean, robust Bayesian analysis of, with partial prior information      240
Multivariate normal mean, robust Bayesian analysis of, with t-priors      245
Murphy, A.H.      206
Nachbin, L.      408
Nash, J.F., Jr.      281
Naylor, J.C.      262
Negative binomial distribution      562
Negative binomial distribution, conjugate prior for      287
Negative binomial distribution, likelihood function for      28
Nell, D.G.      182
Nelson, W.      353
Neyman — Pearson lemma      524
Neyman, J.      22 23 523—525
No-data problems      7 13 17 19
Noda, K.      537

Noninformative prior      see "Prior distribution"
Normal distribution      559 see
Normal distribution as location density      83
Normal distribution as location-scale density      88
Normal distribution as maximum entropy distribution      93
Normal distribution as scale density      85
Normal distribution, invariance in estimation      410 413
Normal distribution, noninformative prior for      84
Normal form of Bayesian analysis      160
Normal mean      559
Normal mean, admissibility and generalized Bayes estimation      543 550 552
Normal mean, admissibility of sample mean      548
Normal mean, Bayesian analysis with noninformative priors      137 289
Normal mean, Bayesian analysis with normal priors      127
Normal mean, Bayesian analysis with normal priors, estimation      136
Normal mean, Bayesian analysis with normal priors, finite action problems      166
Normal mean, Bayesian analysis with normal priors, HPD credible set      140 208
Normal mean, Bayesian analysis with normal priors, one-sided testing      147 164 210
Normal mean, Bayesian analysis with normal priors, posterior robustness      208 210 211 212
Normal mean, Bayesian analysis with normal priors, testing a point null      150 211 212 293
Normal mean, Bayesian analysis with t-priors      246 268
Normal mean, continuous risk functions in estimation      545
Normal mean, estimating a positive      135
Normal mean, gamma minimax estimation      216
Normal mean, invariant estimation      394 399
Normal mean, invariant one-sided testing      394 396
Normal mean, limited translation estimates      219
Normal mean, minimax estimation      350
Normal mean, minimax one-sided testing      349
Normal mean, minimax sequential estimator      501
Normal mean, ML-II prior for      235
Normal mean, optimal sample size in estimation      435
Normal mean, optimal sample size in testing      437
Normal mean, robust Bayesian analysis      239
Normal mean, sequential estimation with normal priors      447
Normal mean, sequential testing with batches      512
Normal mean, SPRT for simple hypotheses      487 494
Normal mean, testing a point null hypothesis      20 148 268
Normal mean, UMP invariant test      428
Normal mean, UMP one-sided testing      529
Novick, M.R.      89 106 183 251
O'Bryan, T.E.      169
O'Hagan, A.      137 249
Objectivity      90 109 125 153 281
Olkin, I.      361
Oman, S.D.      369
Orbits      396
p-values      147 151 155
Paick, K.H.      94 232
Panchapakesan, S.      68
Patel, C.M.      100 169
Pearson, E.S.      22 523—525
Peng, J.C.M.      361 363 370
Peters, S.C.      76 96
Phillips, L.D.      28 503
Pilz, J.      432
Pitman, E.J.G.      399 400
Pitman’s estimator      399 405
Poisson mean      562
Poisson mean, complete class for      553
Poisson mean, conjugate prior for      130
Poisson mean, empirical Bayes estimator      178 297
Poisson mean, inadmissible estimator      360
Poisson mean, minimax estimator      360 369 383
Poisson mean, noninformative prior for      114
Polasek, W.      206 248
Portnoy, S.      537
Post-experimental and pre-experimental      see "Conditional perspective"
Posterior Bayes action      159
Posterior Bayes risk      446 447
Posterior distribution      126 445
Posterior expected loss      157
Posterior mean      134 136 161
Posterior odds ratio      146
Posterior variance and covariance      136 139
Power function      526
Pratt, J.W.      30 138 148 215 252 286 503
Predictive analysis      66 157
Predictive distribution      95 157
Preposterior analysis      432 see
Preposterior analysis, optimal fixed sample size      433 434
Press, S.J.      183 278 361 370
Principle of rational invariance      490
Prior distribution      4 5
Prior distribution, classes of      97
Prior distribution, classes of, $\varepsilon$ -contamination      98 100 197 206 222 232 233
Prior distribution, classes of, in hypothesis testing      154
Prior distribution, classes of, of given functional form      97 197
Prior distribution, classes of, of given structural form      97
Prior distribution, conjugate      130
Prior distribution, construction from marginal      94
Prior distribution, construction from marginal, distance approach      103
Prior distribution, construction from marginal, ML-II approach      101
Prior distribution, construction from marginal, moment approach      101
Prior distribution, construction of subjectively      77
Prior distribution, construction of subjectively, CDF determination      81
Prior distribution, construction of subjectively, elicitation difficulties      76 82 112
Prior distribution, construction of subjectively, given a functional form      78 245
Prior distribution, construction of subjectively, histogram approach      77
Prior distribution, construction of subjectively, multivariate      81 112
Prior distribution, construction of subjectively, relative likelihood approach      77
Prior distribution, construction of subjectively, using the robust form      237 240
Prior distribution, hierarchical      106 180 237 245
Prior distribution, improper      82 87 132 160
Prior distribution, improper, as an approximation      90 229
Prior distribution, improper, inadmissibility of      254
Prior distribution, invariant (right and left) and relatively invariant      84 85 87 290 409 413 416
Prior distribution, least favorable      350
Prior distribution, maximum entropy      90
Prior distribution, ML-II      99
Prior distribution, noninformative      33 82 87 132 135 160
Prior distribution, noninformative and classical statistics      137 406
Prior distribution, noninformative and entropy      92
Prior distribution, noninformative and invariance      83 398 406 409 412 413
Prior distribution, noninformative and minimaxity      309 350 378
Prior distribution, noninformative as an approximation      90 229
Prior distribution, noninformative for binomial parameters      89
Prior distribution, noninformative for location parameters      84
Prior distribution, noninformative for location-scale parameters      88 409
Prior distribution, noninformative for Poisson parameters      114
Prior distribution, noninformative for scale parameters      85
Prior distribution, noninformative in hierarchical situations      187 192
Prior distribution, noninformative, Jeffreys’ prior      87
Prior distribution, noninformative, robustness of      229
Prior distribution, reference informative      153
Prior distribution, robust priors      228 236 245
Prior distribution, robustness of      see "Robustness"
Proschan, F.      136
Purves, R.A.      159 259
R-better      10
R-equivalent      10
Rabena, M.      231
Raiffa, H.      53 57 68 82 130 151 160 277 281 510
Ralescu, D.      550
Ralescu, S.      550
Ramsay, J.O.      251
Ramsey, F.P.      121
Randomized decision rules      12 18 36 40 315 348 397
Rao — Blackwell theorem      41
Rao, C.R.      41 169 172 178 365 550
Rationality      120 198
Rationality and invariance      390
Rationality of Bayesian analysis      120 198
Rationality of game theory and minimax analysis      308 318 371
Rationality, type II      34
Ray, S.N.      455
Reilly, A.      183
Reinsel, G.C.      172 178 365
Restricted risk Bayes principle      22
Rewards      47

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