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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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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, 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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