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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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Estimation, monotone 534 Estimation, sequential 466 480 Ewing, G.M. 92 Exchangeability 104 Exponential distribution 560 Exponential distribution in a classification problem 357 Exponential distribution, conjugate prior for 287 Exponential distribution, invariant estimation for 388 394 396 Exponential distribution, minimax test for 351 Exponential family 526 542 Exponential family, complete classes for 538 539 540 542 550 Exponential family, monotone likelihood ratio of 526 Extended Bayes rules 354 Extensive form of Bayes analysis 160 Faith, R.E. 361 Farrell, R.H. 422 537 539 543 546 547 549 550 Ferguson, T.S. 65 121 346 383 499 545 Fienberg, S. 169 183 Final precision see "Initial and final precision" Fine, T. 199 286 Finite action (multiple decision) problems 163 325 530 Finite action (multiple decision) problems in game theory 325 Finite action (multiple decision) problems, Bayes 163 Finite action (multiple decision) problems, classification 165 357 Finite action (multiple decision) problems, monotone 530 Fishburn, P.C. 50 121 206 Fisher information 87 Fisher information, expected 87 88 224 Fisher information, observed 224 Fisher, R.A. 26 31 35 88 388 Fixed sample size look ahead procedure 457 459 461 Formal Bayes rule 254 Formal Bayes rule, admissibility and inadmissibility of 254 Forrester, J.S. 120 151 Fox, M. 423 550 Fractiles 79 162 Fraser, D.A.S. 26 251 260 261 388 Freedman, D.A. 106 259 Freeman, P.R. 268 French, S.G. 275 277 281 Frequentist perspective 9 22 25 26 27 29 33 44 213 Frequentist perspective and inadmissibility 257 Fristedt, B. 435 Fundamental identity of sequential analysis 489 Games 310 Games, admissible and Bayes strategies for 316 Games, equalizer strategy for 322 325 337 379 Games, finite 325 Games, finite strategy space for II 331 354 Games, finite strategy space for II, lower boundary point 335 Games, finite strategy space for II, minimax theorem 345 Games, finite strategy space for II, risk set 331 Games, finite, simple solution for 326 Games, loss function for 311 316 Games, maximin and minimax strategies for 317 Games, maximin and minimax values of 317 Games, players of 310 Games, randomized strategies for 315 Games, solving 319 Games, solving, direct method 319 Games, solving, finite games 325 Games, solving, guess method 321 322 Games, solving, S-games 331 Games, solving, statistical games 349 Games, statistical 347 Games, strategies for 310 Games, strictly determined 318 Games, two-person zero-sum 311 Games, value of 317 Gamma distribution 560 Gamma distribution, as scale density 85 Gamma distribution, conjugate prior for 287 Gamma distribution, invariant estimation 400 Gamma distribution, noninformative prior for and inadmissibility 255 Gardenfors, P. 199 Gatsonis, C.A. 66 261 Gaver, D.P. 232 Geertsema, J.C. 581 Geisser, S. 89 90 158 203 249 Generalized Bayes rules 160 Generalized Bayes rules and invariance 410 Generalized Bayes rules and minimaxity 350 Generalized Bayes rules, admissibility and inadmissibility of 254 549 550 552 553 557 Generalized Bayes rules, complete classes of 542 Generalized Bayes rules, identifying 543 Generalized maximum likelihood estimator 133 Genest, C. 277 281 Geometric distribution 562 Geometric distribution, as maximum entropy distribution 92 George, E.I. 369 Ghia, G.D. 539 Ghosh, B.K. 435 495 Ghosh, J.K. 225 Ghosh, M. 361 370 543 550 Gifting, J.C. 435 Gilliland, D.C. 169 537 Giron, F.J. 199 Girshick, M.A. 327 346 355 379 380 384 444 Gleser, L.J. 369 Goel, P.K. 108 183 Goldstein, M. 197 284 Good, I.J. 34 35 66 76 80 94 99 106 110 113 119 148 156 168 183 195 198 199 203 206 215 249 252 284 Govindarajulu, Z. 435 Groenewald, P.C.N. 182 280 281 Group decision making 278 Groups of transformations 391 Groups of transformations, additive (or location) 392 399 Groups of transformations, additive (or location), Haar densities for 429 Groups of transformations, affine 392 401 407 Groups of transformations, affine, Haar densities for 409 Groups of transformations, matrix groups 429 Groups of transformations, matrix groups, Haar densities for 429 Groups of transformations, multiplicative (or scale) 392 Groups of transformations, multiplicative (or scale), Haar densities for 429 Groups of transformations, orthogonal 426 428 Groups of transformations, permutation 392 Gupta, A.K. 571 Gupta, S.S. 68 217 541 Gutmann, S. 361 Haar densities 406 409 425 429 430 Haff, L.R. 160 169 178 361 365 369 Hagen, O. 50 Hald, A. 350 Hall, W.J. 89 132 Halmos, P.R. 408 Hammersley, J.M. 265 Handscomb, D.C. 265 Harris, J.E. 183 Hartigan, J.A. 83 87 197 205 206 225 Hawkes, J.S. 369 Heath, D. 258 259 Heyde, C.C. 225 Hide and seek 380 Hierarchical Bayes analysis 180 Hierarchical Bayes analysis for exchangeable normal means 183 Hierarchical Bayes analysis for general normal means 190 Hierarchical Bayes analysis, comparison with empirical Bayes 193 Hierarchical priors see "Prior distribution" Highest posterior density (HPD) credible set 140 144 Highfield, R.A. 94 Hildreth, C. 268 Hill, B. 90 135 148 177 183 195 206 223 228 252 258 261 Hinde, J. 26 Hinkley, D.V. 23 67 250 Hirschmann, I.I. 544 Hoadley, B. 169 Hodges, J.L., Jr. 148 219 221 Hoeffding, W. 469 Hoffman, K. 550 Hogarth, R.M. 76 81 277 281 Holland, P. 169 183 Hooper, P.M. 418 Hora, R.B. 413 Howard, R.A. 277 Hsiao, P. 217 Huber, P.J. 69 207 248 Hudson, H.M. 169 361 363 364 Hui, S. 168 169 Hunt — Stein theorem 420 422 Huzurbazar, V.S. 35 Hwang, J.T. 172 251 361 363 369 370 549 550 554 Hylland, A. 281 Hyperparameters 99 102 180 Hyperplane 338 Hypothesis testing in Bayesian decision theory 163 Hypothesis testing in Bayesian decision theory for " 164 Hypothesis testing in Bayesian decision theory of simple hypotheses 355 Hypothesis testing in Bayesian inference 145 268 Hypothesis testing, error probabilities 23 25 30 44 148 356 Hypothesis testing, invariant 395 404 Hypothesis testing, invariant, UMP invariant 404 428 Hypothesis testing, minimax 351 356 Hypothesis testing, most powerful tests 357 524 Hypothesis testing, multiple 157 165 Hypothesis testing, one-sided 147 Hypothesis testing, point null hypothesis 20 148 268 Hypothesis testing, point null hypothesis, Bayesian and classical 20 147 148 155 164 508 Hypothesis testing, point null hypothesis, complete class 539 Hypothesis testing, point null hypothesis, Jeffreys’ or Lindley’s paradox 156 Hypothesis testing, power function 526 Hypothesis testing, sequential 462 477 481 500 Hypothesis testing, significance 20 21 28 202 203 Hypothesis testing, simple hypotheses 25 355 481 524 Hypothesis testing, size 13 526 Hypothesis testing, size, inadequacies of 20 21 23 30 44 202 Hypothesis testing, SPRT 481 Hypothesis testing, SPRT for one-sided hypotheses 500 Hypothesis testing, SPRT for simple hypotheses 481 Hypothesis testing, test function 355 Hypothesis testing, two-sided testing 538 Hypothesis testing, uniformly most powerful tests 526 Hypothesis testing, uniformly most powerful tests for one-sided hypotheses 527 Ighodaro, A. 543 Improper prior see "Prior distribution" Inadmissibility 10 Inadmissibility and long run evaluations 257 Inadmissibility of Bayes rules in S-games 382 Inadmissibility of formal Bayes rules 254 Inadmissibility of generalized Bayes rules 254 549 552 Inadmissibility of invariant rules 422 Inadmissibility of minimax rules 360 371 Inadmissibility, relationship to coherency 259 Inadmissibility, verification of 550 Inadmissibility, verification of, of normal means 552 Inadmissibility, verification of, of Poisson means 553 Incoherency 259 Independent opinion pool 273 Inference 7 20 see Inference, loss functions for 64 166 261 Inference, predictive 157 Initial and final precision 26 30 see Interim analysis 504 519 Invariance 19 388 see Invariance and minimaxity 418 Invariance and noninformative priors 390 398 406 409 414 424 Invariance in decision problems 393 Invariance in estimation 400 405 Invariance in hypothesis testing 395 404 Invariance principle 390 Invariance, location parameter problems 397 402 404 423 Invariance, location-scale problems 401 403 Invariance, scale parameter problems 400 402 424 428 Invariance, too much 421 424 431 Invariant decision rules 395 see Invariant decision rules, admissibility and inadmissibility of 422 Invariant decision rules, best 397 409 Invariant decision rules, confidence rules 414 Invariant decision rules, constancy of risk functions 396 Invariant decision rules, Pitman’s estimator 400 405 Invariant function 402 Invariant prior distribution 84 85 87 Isaacs, H.H. 206 Isaacson, D. 228 Isii, K. 537 Isomorphism 409 Jackson, D.A. 217 Jackson, P.H. 183 James, W. 256 361 364 422 543 549 Jaynes, E.T. 35 83 89 90 91 92 94 110 119 Jeffrey, R. 9 277 283 Jeffreys, H. 29 35 76 83 87 88 89 90 110 119 133 151 153 156 203 225 249 270 Jenkins, G.M. 503 Jennrich, R.I. 100 Jensen’s Inequality 40 343 Jewell, W.S. 132 136 169 Johnson, J.D. 265 Johnson, R.A. 225 Johnson, R.W. 361 Johnstone, I.M. 225 265 553 554 Jones, A.J. 281 314 Joshi, S.N. 225 Joshi, V.M. 550 Judge, G. 369 Kadane, J.B. 76 96 206 251 266 Kahneman, D. 76 82 106 198 Karlin, S. 530 532 533 535 538 550 Keener, R.W. 435 Keeney, R.L. 53 57 68 Kelley, T.L. 168 Kempthorne, P.J. 353 Kiefer, J. 26 27 122 397 415 420 431 477 481 501 541 Kloeck, T. 265 Knill-Jones, R. 277 Kozek, A. 537 Kraft, C.H. 286 Kudo, H. 215 413 Kuo, L. 107 183 Kusama, T. 537 La Motte, L.R. 550 Laird, N.M. 100 101 178 Lalley, S. 553 Lane, D.A. 90 121 259 Laplace, P.S. 82 83 89 187 225 Large sample approximations 223 Large sample approximations in hypothesis testing 156 Large sample approximations in sequential analysis 477 Large sample approximations to posterior distribution 142 170 224 Large sample approximations, comparing Bayes to classical 125 Larson, R.E. 435 Lauritzen, S.L. 106 Le Cam, L. 120 122 225 346 537 546 Leamer, E.E. 156 206 248 Least favorable prior distribution 350 Left invariant Haar density 406 409 429 430 Lehmann, E.L. 37 65 68 88 144 148 219 221 353 420 Lehn, J. 217 Lempers, F.B. 156 Leonard, T. 100 101 169 178 183 Lepage, R. 495 Liar’s poker 381 Likelihood function 27 Likelihood function in sequential setting 503 Likelihood principle 27 34 505 Likelihood principle and censoring 30 Likelihood principle and noninformative priors 89 Likelihood principle, derivation of 31 Likelihood principle, implies stopping rule principle 503 Likelihood principle, implies sufficiency 37 Likelihood principle, limitations of 29 32 Likelihood principle, satisfied by Bayesian analysis 126 160
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