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Bernardo J.M., Smith A.F.M. — Bayesian Theory
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Название: Bayesian Theory
Авторы: Bernardo J.M., Smith A.F.M.
Аннотация: This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called ‘prior ignorance. The work is written from the authorss committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2000
Количество страниц: 586
Добавлена в каталог: 12.04.2010
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Предметный указатель
Gilio, A. 89 263 371 516
Gilks, W.R. 353 355 426 516 549
Gillies, D.A. 2 516
Gilliland, D.C. 373 516
Girelli-Bruni, E. 9 516
Giron, F.J. viii 99 104 373 374 419 497 500 516
Girshick, M.A. 91 446 498 517
Godambe, V.P. 10 374 517
Goel, P.K. 10 104 158 276 371 373 425 496 517
Goicoechea, A. 104 517
Goldstein, M. 11 94 163 373 426 455 517 518
Gomez, E. 417 518
Gomez-Villegas, M.A. viii 371 417 518
Good, I.J. 9 10 11 75 90 91 94 99 100 102 154 228 263 360 373 374 390 458 518 519 536
Goodman, B.C. 375 509
Goodwin, P. 375 519
Gordon, N.J. 370 519
Goutis, C. 468 519
Grandy, W.T. 10 519 546
Grayson, C.J. 10 53 519
Green, P.J. 353 356 497
Grenander, V. 374 519
Grieve, A.P. 11 426 519 540
Groenewald, P.C.N. 104 158 506
Group communication, decision making 5 8 92 102—104 166 236 237 275 424 425
Groups of transformations 362 454 460
Growth curves 220 382
Gu, C. 374 519
Gulati, C.M. 104 517
Gupta, S.S. 10 519 520
Gutierrez-Pena, E. 277 520
Guttman, I. 158 230 418 484 508 520 537
Haag, J. 235 520
Haar measure prior 362 see
Hacking, I. 99 102 520
Hadley, G. 10 520
Hagen, D. 96 490
Haimes, Y. 104 500
Hald, A. 374 520
Haldane, J.B.S. 315 362 520
Hall, W.J. 228 283 502
Hall, W.K. 362 535
Halmos, P.R. 451 520
Halter, A.N. 10 520
Harris, J.E. 374 508
Harrison, P.J. 10 374 520 539 552
Harsany, J. 104 520
Hartigan, J.A. 9 99 130 163 164 250 289 359 360 362 371 455 506 520 521
Hartley, R. 10 104 513
Hasminski, R.Z. 289 523
Hastings, W.K. 356 521
Hays, W.L. 375 509
Heath, D.L. 88 90 162 172 521
Helly's theorem 126 173 213
Henrion, M. 375 534
Hens, T. 84 521
Hernandez, A. 451 500
Herstein, I.N. 91 521
Hewitt, E. 235 521
Hewlett, P.S. 219 521
Heyde, C.C. 289 521
Hierarchical model and binomial parameters 223
Hierarchical model and normal parameters 224—226 383
Hierarchical model, prior xiii 7 222—226 371—373 383 480
Highest probability density (HPD) region see "Credible region"
Hildreth, C. 425 521
Hill, B.M. 11 162 227 228 250 371 373 420 496 521 522
Hill, S.D. 362 546
Hill, W.J. 417 498
Hills, S.E. 239 295 338 348 355 515 522
Hinkelmann, K. 10 522
Hinkley, D.V. 368 376 445 480 485 487 502 522
Hipp, C. 203 522
histogram 351
history 10 356 357
Hjort, N.L. 228 522
Hoadley, B. 373 522
Hodges, J.S. 10 11 104 263 419 513 514 522
Hogarth, R. 104 375 522
Holland, G.D. 2 522
Hop, J.P. 349 549
Howard, J.V. 455 518
Howson, C. 10 522
Hsu, J.S.J. 345 374 375 529 530
Hull, J. 87 91 523
Huseby, A.B. 104 523
Hutton, I. 44 535
Huzurbazar, V.S. 203 523
Hwang, J.T. 258 523
Hwang, J.T.G. 465 469 500 541
Hylland, A. 104 523
Hypergeometric distribution, model 115 172 322 428
Hypergeometric, function 338 363
Hyperparameter 224 270 271 275 339 372
Hypothesis 2 262 263 380—382 390
Hypothesis testing xiv 8 9 445 469—475 see
Hypothesis testing and Lindley's paradox 394 406 407 415 416 422
Hypothesis testing in Bayesian inference 262 263 391—397
Hypothesis testing of point null hypothesis 394 406 407 414—416
Hypothesis testing, composite versus composite 392—394 396 397
Hypothesis testing, critical region 470
Hypothesis testing, inadequacies of 472—475
Hypothesis testing, likelihood ratio test 476 487—488
Hypothesis testing, minimax 472
Hypothesis testing, one-sided tests 396 397 472
Hypothesis testing, power function 470 473
Hypothesis testing, simple versus composite 392 394
Hypothesis testing, simple versus simple 392 471
Hypothesis testing, size of a test 471
Hypothesis testing, test procedure 470
Hypothesis testing, two-sided tests 473
Hypothesis testing, unbiased test 473
Hypothesis testing, uniformly most powerful test 472 473
Hypothesis, alternative 233 380 391 469 470
Hypothesis, composite 391 392 394 471—475
Hypothesis, null 233 394 414 416 469 470
Hypothesis, simple 380 391 392 394 471 475
Ibragimov, I.A. 289 523
Identifiability 239
Image analysis 5 374
implementation issues xii 263 264
Importance sampling xiii 8 264 340 348—350
Improper prior distribution 276 277 321 357—367 421—424 449 469
Improper probabilities 163
Inadmissibility 367 see
Incoherence see "Coherence"
Independence and dependence xi 167 168
Independence of random quantities 113 130 172—190 194—197
Independence, characterisation of 37—38
Independence, conditional 45—47
Independence, mutual 46
Independence, pairwise 28
Induction, a problem of 322 323
Inference as a decision problem 6 67—81 92 102 420 444
Inference, Bayesian 241—426
Inference, comparative 376 445
Inference, conditional and unconditional xiv 374 445 452 468 475 478 479
Inference, critical issues xiii 374 375 418—426
Inference, fiducial xiv 9 444 456—458 461 484 486
Inference, likelihood xiv 9 444 454—456 461
Inference, pivotal 458 459 461
Inference, pure problem of 6 67—81 102
Inference, statement, answer 255
Inference, structural 459—461
Inference, summaries xii 255—263
Inferential processes, Bernoulli, binomial model 248 249 270—274 276 277 279—282 436
Inferential processes, exponential model 438
Inferential processes, linear regression 442
Inferential processes, multinomial model 441
Inferential processes, multivariate normal model 441
Inferential processes, negative binomial model 437
Inferential processes, summaries xiv 436—442
Inferential processes, uniform model 438
Inferential processes, univariate normal model 439 440
Infinite exchangeability see "Exchangeability"
Influential observations 418 see
information 6 17 77—81 147—159 207—209 298—300 360 see
Information and the exponential family xii 207—209
Information matrix see "Fisher information"
Information, amount of x xi 6 77—81
Information, expected 80 91 158 159
Information, missing 304 308 324 362
Information, perfect 65 149 300
Information, theories of 10 91 92
Information, value of 65 147—149
Initial and final precision 478 479
Insufficient reason, principle of see "Bayes — Laplace postulate"
Insurance 373
Interquantile range 112
Intersubjective 102—104 166 237 see
Interval estimation (Bayesian) see "Credible regions"
Interval estimation (non-Bayesian) xiv 445 465—469
Interval estimation (non-Bayesian), confidence limits for 465—469
Interval estimation (non-Bayesian), most selective interval 467
Interval estimation (non-Bayesian), shortest confidence interval 467
Invariance 7 454
Invariance and Laplace approximation 344 345
Invariance and noninformative priors 358 362 366
Invariance and representation theorems 181—190 204
Invariance in estimation 454
Invariance of preferences 26
Invariant prior distribution 358 362
Inverted chi-squared distribution 119 431
Inverted gamma distribution 119 431
Inverted Pareto distribution 120 432
Irony, T.Z. 11 258 374 376 491 523
Isaacs, G.L. 261 523
Isaacson, D. 371 533
Iterative quadrature see "Numerical quadrature"
Iversen, G.R. 9 523
Iyengar, N.S. 10 517
Jacknife 371
Jackson, J.E. 375 523
Jackson, P.H. 10 261 523 535
Jaffray, J.Y. 99 500
James, W. 449 523
Jaynes, E.T. 10 90 227 357 363 365 366 375 451 468 523
Jefferys, W.H. 371 495
Jeffrey's rule 94
Jeffrey, R.C. 10 94 524
Jeffreys' prior, rule 314 315 357—362 see
Jeffreys, B.S. 73 153 208 341 524
Jeffreys, H. 9 73 90 98 153 208 263 288 314 315 322 341 358 359 360 361 362 366 370 414 419 478 524 553
Jenkins, G.M. 250 455 492
Jennings, D.E. 419 501
Jewell, W.S. 373 524
Johnson, N.L. 114 133 524
Johnson, R.A. 289 524
Johnson, W. 418 524
Johnstone, I.M. 289 521
Joshi, V.M. 11 250 524
Justice, J.M. 10 525
Kadane, J.B. 10 11 91 98 104 130 160 162 239 243 250 341 344 371 373 375 411 472 494 505 508 525 526 543 544 549 550 551
Kagan, A.M. 184 525
Kahneman, D. 96 375 525
Kalbfleish, J.G. 455 481 484 525
Kapur, J.M. 10 525
Karlin, S. 417 525
Kashyap, R.L. 360 526
Kass, R.E. 10 289 341 348 358 361 373 417 513 526 549
Keeney, R.L. 10 91 104 526
Kelly, J.S. 104 526
Kempthome, P.J. 371 526
Kent, J.T. 374 532
Kernel density estimate 351 355
Kernel of a density 129
Kesavan, H.K. 10 525
Kestemont, M.-P 228 526
Keynes, J.M. 9 90 98 100 526
Khintchine, A.I. 235 526
Kiefer, J. 480 526
Kihlstrom, R.E. 10 499
Kim, K.H. 104 526
Kimeldorf, G.S. 228 526
Kingman, J.F.C. 106 182 527
Kirby, A.J. 353 355 516
Klein, R. 483 527
Klein, R.W. 420 527
Kleiter, G.D. 9 527
Kloek, T. 349 527 550
Klugman, S.A. 9 527
Knill-Jones, R. 95 546
Koch, G. 236 527
Kogan, N. 104 527
Kohn, R. 374 491
Kolmogorov, A.N. 485 527
Koopman, B.O. 98 527
Koopman, L.H. 203 527
Korsan, R.J. 426 527
Kotz, S. 114 133 524
Kraft, C. 90 527
Krantz, D.H. 85 90 104 527 532
Krasker, W.S. 420 527
Kuechler, U. 236 527
Kuhn, T.S. 93 527
Kullback, S. 6 76 91 208 527
Kyburg, H.E. 10 87 99 102 527 528
Lack of memory property 187 190
Lad, F. 160 163 528
Ladalla, J.N. 289 524
LaMotte, L.R. 11 528
Lane, D.A. 162 485 522 528
Laplace approximation xiii 8 264 340—345 455
Laplace's rule of succession 272 322 323
Laplace, P.S. 2 9 89 272 288 357 528
Large sample approximations see also "Asymptotic analysis"
Large sample approximations to posterior distribution 285—297 314 365
Large sample approximations, comparing Bayes to classical 486
Larkey, P. 104 525
Laud, P. 228 509
Lauritzen, S.L. 95 227 236 426 507 527 528
Lavalle, I.H. 9 10 87 528
Lavine, M. 228 371 483 528
Law 10 374
Law of Large Numbers 126
Law of the iterated logarithm 127
Lawrie, T.D.V. 44 535
Le, H. 370 536
Le, N.D. 374 499
Learner, E.E. 10 263 417 528
Least favourable prior distribution 449 see
Lebesgue integration, measure 111 133 141 161—163
LeCam, L. 288 485 528 529
Lecoutre, B. 10 529
Lee, P.M. 9 529
Lee, T.D. 420 545
Lee, T.M. 247 515
Lehmann, E.L. 15 68 237 238 465 529
Leibler, R.A. 76 91 527
Lejeune, M. 485 529
Lempers, F.B. 10 263 529
Length, operational definition of 82 83
Lenk, P.J. 228 529
Leonard, T. 10 228 238 345 373 374 375 407 498 529 530
Levine, R.D. 10 530
Lewis, S.M. 353 539
Ley, E. 426 530
Li, B. 341 553
Lientz, B.P. 417 508
Likelihood function 7 43 173 174 177 185 243 450 480 481
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