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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
Likelihood function, approximation for large samples 485 486
Likelihood function, conditioned 48
Likelihood function, integrated 245 390 470
Likelihood inference xiv 9 444 454—456 461
Likelihood principle 249 250 454
Likelihood principle and noninformative priors 367
Likelihood principle and stopping rules 250—255
Likelihood principle, derivation of 249 250
Likelihood principle, implies sufficiency 455
Likelihood principle, satisfied by Bayesian analysis 249
Likelihood principle, violation of 463
Likelihood ratio 49 392 455 470 476 487
Limit theorems xi 125—127
Limiting frequency 173 174 177 179 450—454
Lindgren, B.W. 10 530
Lindley's paradox see "Hypothesis testing"
Lindley, D.V. viii 9 10 11 42 62 87 88 90 91 103 104 158 159 160 261 263 272 289 338 345 359 364 367 373 374 375 394 417 449 455 457 460 472 484 486 496 497 499 501 504 530 531 537
Lindman, H. 11 263 371 425 509
Linear models 5 10 221 222 442 see
Linear theory (based on expectation operator) 162 163
Linear transformation of utilities 55
Linnik, Y.V. 184 525
Liseo, B. 371 481 531 532
Little, R.J.A. 374 532
Lo, A.Y. 228 371 374 508 532
Location-scale parameters 320 362 379 380 415 458
Logarithmic divergence 76 91 278 279 286 287 358 402 416 476
Logistic distribution 122 239 240 349 433
Logistic model 220 382
Logit model 219 220 382
Lorimer, A.R. 44 535
Loss functions 256—263 445—449 461
Loss functions for inference problems 256—263
Loss functions from utility functions 256 391 396 445
Loss functions, absolute value 257
Loss functions, linear 257 396 397
Loss functions, logarithmic divergence 279
Loss functions, quadratic 85 88 257 300 301 397 401 406
Loss functions, standardised quadratic 301
Loss functions, zero-one 257 405
Lottery see "Option"
Lottery, canonical 85
Louter, A.S. 349 549
Luce, R.D 11 85 90 91 96 103 104 527 532
Lusted, L.B. 10 532
Lwin, T. 373 532
Maatta, J. 468 532
Machina, M. 91 96 532
Maekelaeinen, T. 373 499
Mahalanobis distance 416
Main, P. 370 371 518 532
Makov, U.E. 373 374 515 532 549
Malitz, J. 90 501
Mardia, K.V. 374 532
Marginal distribution 128 166
Marginalisation paradoxes 363 364 479—481
Marginalisation procedures xiv 128 445
Marinell, G. 10 532
Maritz, J.S. 373 532
Markov chain Monte Carlo xiii 8 264 340 353—356
Marriage problem 61—63
Marriott, J.M. 348 426 532 533
Marschak, J. 91 104 494 533
Martin, J. 371 541
Martin, J.J. 10 533
Martinez, L. 419 516
Martz, H.F. 10 533
Maryak, J.L. 258 546
Masreliez, J.L. 370 533
Mathematics, the role of xi 30 31 49 50 82 85 105 106 141 142 160—164 170 226—229
Matheson, J.E. 10 375 546
Mathiasen, P.E. 484 533
Maximisation of expected utility 52 56 90 91 146 147 256 386 388
Maximum entropy, procedures 10 209 366
Maximum likelihood estimate 288 461 465
Maximum likelihood estimate, asymptotic distribution of 485
Mazloum, R. 160 533
McCardle, K.F. 104 535
McCarthy, J. 91 533
McClintock, C.G. 91 494
McCulloch, R.E. 232 367 374 417 418 515 533
McDunnough, P. 289 512
McKillop, J.H. 44 535
McNeil, A.J. 353 355 516
Mean 112 131 357 258 461 see
Mean squared error 462—465
Measure theory 111 133 141 161—163 177
Median 112 257 258 461
Medical diagnosis 44 45
Meeden,G. 160 366 371 533
Meinhold, R. 374 533
Mendel, M.B. 236 491 533
Mendoza, M. viii 295 307 362 495 533
Meng X.-L. 374 533
Merkhofer, M.W. 375 533
Meta-analysis 374
Metropolis — Hastings algorithm 355 356
Metropolis, N. 356 533
Meyer, D.L. 10 533
Migon, H.S. 374 512 552
Miller, M. 374 519
Mills, J.A. 374 534
Milnor, J. 91 521
Minimax principle, procedures 360 449 461 472
Missing data 374
Missing information 304 308 324 362
Mitchell, T.J. 160 232 534
Mixtures see "Representation theorems"
Mixtures, finite 279—283 374 462
Mockus, J. 10 534
MODE 112 257 258 461
Model comparison and Bayes factors xiii 390—394 405 414 417 422—424
Model comparison and covariate selection xiii 407—409
Model comparison as a decision problem xiii 386—409
Model comparison perspectives, closed view 384
Model comparison perspectives, completed view 385
Model comparison perspectives, open view 385
Model comparison, approximation by cross validation xiii 403—407 409 420—424
Model comparison, general utilities for xiii 395—402
Model comparison, perspectives on xiii 383—385
Model comparison, zero-one utilities for xiii 389—395
Model rejection, discrepancy measures for xiv 412—417
Model rejection, through model comparison xiv 409—412
Modelling xi 7 165—240
Modelling, critical issues xii 237—240
Modelling, scientific 237 238
Modelling, technological 237 238
Modelling,and exchangeability 167—181
Modelling,and invariance 181—190
Modelling,and partial exchangeability 209—222
Modelling,and remodelling xiv 377—426
Modelling,and sufficient statistics 191—207
Models 7 114
Models and invariance xii 181—190
Models, choice of xiv 8 377—409 419 420 445 486—488
Models, comparison of xiii 377—409 483
Models, criticism of 419 420 483
Models, elaboration of xii 229—232
Models, empirical 237 238
Models, explanatory 237 238
Models, nonparametric xii 228
Models, parametric xii 7 172—234 242—255 380—383
Models, predictive 165—167 243 244
Models, ranges of xiii 8 277—283
Models, rejection of xiv 409—417
Models, role of 237 238
Models, simplification of xii 233 234
Mohammad-Djafari, A. 10 534
Moment-generating function 114
Moments 112 113 131 132
Monahan, J.E 455 534
Monetary bets 86—88 162
Monotone continuity of uncertainty relation 107
Monotonicity of uncertainty relation 27
Monte Carlo methods see "Stochastic simulation"
Moore, P.G. 87 91 523
Morales, D. 160 536
Morales, J.A. 10 239 534
Morcillo, C. 419 516
Moreno, E. viii 371 394 451 500 534
Morgan, M.G. 375 534
Morgenstern, O. 84 90 91 446 550
Morris, C.N. 206 343 344 373 509 534
Morris, M.D. 160 534
Morris, P.A. 104 534
Morris, W.T. 10 534
Mortera,J. 104 371 374 394 495 505 534
Moses, L.E. 10 91 501
Mosteller, F. 9 81 534
Mouchart, M. 9 10 130 164 239 373 374 420 512 534
Mueller, P. 374 552
Muirhead, C.R. 230 535
Mukerjee, R. 324 359 516 535
Muliere, P. 9 501
Multinomial distribution and exchangeability xi 176 177
Multinomial distribution, conjugate analysis of 441
Multinomial distribution, conjugate family for 441
Multinomial distribution, inferential process for 441
Multinomial distribution, model 133 134 176 177 216 433
Multinomial distribution, reference distributions for 336 441
Multinomial—Dirichlet distribution 135 136 433
Multinomial—Dirichlet distribution as predictive distribution 441
Multiple regression 221 222 383 442
Multivariate analysis 5 10 374
Multivariate distributions 133—141 433—435
Multivariate normal distribution and exchangeability xi 185 186
Multivariate normal distribution as approximation to posterior distribution 286—297 314 365
Multivariate normal distribution as prior distribution 441 442
Multivariate normal distribution, conjugate analysis of 441
Multivariate normal distribution, conjugate family for 441
Multivariate normal distribution, inferential process for 441 449
Multivariate normal distribution, model 136—138 140 365 434
Multivariate normal distribution, reference distributions for 441
Multivariate normal distribution, sufficient statistics for 441
Multivariate normal-gamma distribution 140 435
Multivariate normal-gamma distribution as prior distribution 442
Multivariate normal-Wishart distribution 140 435
Multivariate normal-Wishart distribution as prior distribution 441
Multivariate Student distribution 139 140 435
Multivariate Student distribution as marginal posterior distribution 441
Multivariate Student distribution in linear model 442
Munoz, J. viii
Murphy, A.H. 71 535
Murray, R.G. 44 535
Mutual independence 46
Myerson, R.B. 89 535
Nakamizo, T. 10 374 543
Nakamura, Y. 99 535
Narens, L. 84 90 532 535
Nau, R.F. 104 371 535
Naylor, J.C. 346 347 426 533 535 545
Nazaret, W.A. 371 537
Negative-binomial distribution 116 119 429
Negative-binomial distribution, conjugate analysis of 437
Negative-binomial distribution, conjugate family for 437
Negative-binomial distribution, inferential process for 437
Negative-binomial distribution, reference distributions for 437
Negative-binomial distribution, sufficient statistics for 437
Negative-binomial-beta distribution 118 429
Neighbourhood of distributions 370
Nelder, J.A. 488 535
Newman, J.R. 104 509
Neyman factorisation criterion 193—195
Neyman — Pearson lemma 471 472
Neyman, J. 195 446 450 471 480 535
Nicolau, A. 359 535
No-data problems 446
Non-Bayesian theories, alternative approaches xiv 445—460
Non-Bayesian theories, hypothesis testing xiv 469—475
Non-Bayesian theories, interval estimation xiv 465—469
Non-Bayesian theories, point estimation xiv 460—465
Non-Bayesian theories, significance testing xiv 475—478
Non-central chi-squared distribution 121 431
Non-informative prior 277 298 314 357—367 see
Non-informative prior, invariant prior 358 361 362 366
Non-informative prior, Jeffreys' prior 314 315 357—362
Nonparametric models, inference xii 5 228
Normal distribution and exchangeability xii 181—185
Normal distribution as approximation to posterior distribution 286—297 314 365
Normal distribution as maximum entropy choice 209
Normal distribution as prior distribution 253 300
Normal distribution, "biased" stopping rule for 253—255
Normal distribution, conjugate analysis of 274 439 440
Normal distribution, conjugate family for 268 439 440
Normal distribution, inferential process for 253—255 297 361—365 369 394 396 397 401 402 406 407 415 416 439 440 446 453 473
Normal distribution, model 7 121 123 136 155—157 181—185 196 216 432 459 463 464 478 480
Normal distribution, reference distributions for 328—333 439 440
Normal distribution, sufficient statistics for 196 199 439 440 462
Normal-gamma distribution 136 434
Normal-gamma distribution as prior distribution 268
Normand, S.-L. 104 535
Novick, M.R. 10 42 261 362 368 523 531 535 540
Nuisance parameter xiv 245 445 479—481
Numerical approximations xiii 339—356 see
Numerical quadrature xiii 8 264 346—348
O'Hagan, A. 9 10 230 348 370 371 423 495 510 535 536
Objectivity xii 2 3 99—102 236 237 275 298 424 425
Observables xii 7 241—247
Occam's razor 476
Odds 49 357 390 391
Oil wildcatters 53 54
Oliver, R.M. 10 536
Operational perspective x 18 22 51 81—83 85 87 90 94 99 100 102 161 195 235 243 298
Opportunity loss 65 149
Optimal stopping 59—63
Optimisation 10
options 18 19
Options, finite 23—33
Options, generalised xi 141—149
Options, standard 29—33
Ord, K. 407 530
Ordered parametrisation 323 333 364 367
Ordering see "Preference relation"
Origin invariance 187—191
Osiewalski, J. 371 536
Osteyee, D.D.B. 10 536
Outlier 229 230 240 370
Overfitting 420 421
p-values 474—478
Pack, D.J. 11 536
Padgett, W.J. 228 536
Page, A.N. 91 536
PARAMETER 7 173—177 179—190 192—197 220 235 see
Parameter as label of distribution 114—125 133—141
Parameter of conjugate family 265 266
Parameter of interest 245
Parameter, equality 233 234
Parameter, nuisance 245 445 479—481
Parametric, inference 243—247
Parametric, model xii 228 229
Parametric, sufficiency xii 192 193
Pardo, L. 160 536
Parenti, G. 10 536
Pareto distribution 120 141 432
Pareto distribution as prior distribution 438
Parmigiani, G. 160 536
Partial exchangeability xii 7 168—170 208—222
Pascal distribution see "Geometric distribution"
Pathak, P.K. 10 516
Pattern recognition 10
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