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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
Pearson family of distributions 343
Pearson, E.S. 2 446 450 471 536
Peers, H.W. 359 537 552
Pefia, D. 230 418 420 520 537
Peirce, C.S. 81 390 537
Peizer, D.B. 124 537
Pereira, C.A. de B. 136 374 455 493 523 537
Perez, M.E. 371 373 537
Pericchi, L.R. viii 231 369 370 371 373 405 407 422 423 424 534 537 543
Perks, W. 314 315 359 537
Peskun, P.H. 356 537
Petrella, L. 371 532
Petris, G. 162 540
Pettit, L.I. 230 417 418 537 538
Pfanzagl, J. 84 91 489 538
Phadia, E.G. 11 228 510
Pham-Gia, T. 160 538
Phillips, L.D. 10 272 375 509 531 538
Philosophy of science 10
Piccinato, L. 362 376 538
Pierce, D. 468 469 538
Pilz, J. 10 160 538
Pitman estimator 465
Pitman, E.J.G. 203 465 538
Pivotal inference 458 459 461
Plackett, R.L. 219 521
Plante, A. 455 466 538
Poetzelberger, K. 371 538 539
Point estimation (Bayesian) 8
Point estimation (Bayesian) for absolute error loss 257
Point estimation (Bayesian) for linear loss 257
Point estimation (Bayesian) for logarithmic divergence loss 279
Point estimation (Bayesian) for quadratic loss 257
Point estimation (Bayesian) for zero-one loss 257
Point estimation (Bayesian) in inference 257 258
Point estimation (Bayesian), Bayes estimate 257 258 461 465
Point estimation (non-Bayesian) xiv 9 445 460—465
Point estimation (non-Bayesian), best linear unbiased (BLUE) 463
Point estimation (non-Bayesian), bias 359 462—465
Point estimation (non-Bayesian), consistent 312 320 326 353 405 463—465
Point estimation (non-Bayesian), efficiency of 462
Point estimation (non-Bayesian), maximum likelihood (MLE) 288 359
Point estimation (non-Bayesian), minimum variance bound (MVB) 464 465
Point estimation (non-Bayesian), unbiased 348 462—465
Point estimation (non-Bayesian), uniform minimum variance (UMV) 464 465
Poirier, D.J. 376 420 445 538
Poisson distribution as an approximation to the Binomial 76 77
Poisson distribution, characterisation via sufficiency 206
Poisson distribution, conjugate analysis of 274 437
Poisson distribution, conjugate family for 267 268 437
Poisson distribution, inferential process for 437
Poisson distribution, model 116 199 206 429
Poisson distribution, reference distributions for 437
Poisson distribution, sufficient statistics for 437
Poisson-gamma distribution 119 429
Poisson-gamma distribution as predictive distribution 437
Polasek, W. 371 538 539
Pole, A. 10 366 374 538 539
Pollard, W.E. 10 539
Polson, N.G. 9 159 315 370 374 500 539
Poskitt, D.S. 417 539
Posterior distribution 9 43 94 130 175 242—247
Posterior distribution, approximation for large samples 286—297 314 365
Posterior distribution, convergence to correct value 285—287
Posterior distribution, reference see "Reference distribution"
Posterior odds ratio 49 356 390
Power function 470—475
Pragmatism 81
Pratt, J.W. 9 85 87 90 124 250 262 263 376 527 537 539
Precise measurement 285
Precision matrix of multivariate normal distribution 137
Precision matrix of multivariate t distribution 140
Precision, of normal distribution 121 182
Prediction 7 10 407 408 445 454
Prediction, comparative issues xiv 482—485
Prediction, with quadratic loss 300 301 397—399 401 402 406 407
Predictive, distribution 43 243—247 419 483
Predictive, inference 243—247 483
Predictive, model 167 419 444
Predictive, sufficiency 191—193
Preference relation x xi
Preference relation, among decisions 141—147
Preference relation, among options 17—33 52 56
Preference relation, precise measurement of 31—33
Prequential analysis 485 488
Prescriptive theory 4 23 32 95—98
Press, S.J. 9 10 11 104 376 445 483 514 527 539
Prevision 162 163
Price, R. 2
Principle of optimality (Bellman) 61
Prior distribution 9 43 94 130 173—182 185 186 189 190 234 235 241—247 357—367 444 446 450 470 see
Prior distribution and modelling xii 165—235
Prior distribution, "objective" 275 298 357
Prior distribution, "vague" 8 357—367
Prior distribution, approximation 279—285
Prior distribution, conjugate see "Conjugate prior family of distributions"
Prior distribution, elicitation of 5 160 234 235 370 375
Prior distribution, hierarchical 222—226 371 372 383
Prior distribution, invariant and relatively invariant 358 361 362
Prior distribution, Jeffreys' prior 314 315 357—362
Prior distribution, least favourable 449
Prior distribution, maximum entropy 365
Prior distribution, non-informative 357—367
Prior distribution, possible dependence on stopping rule 252 255
Prior distribution, reference 298 300—339 361 363—365 416
Prior distribution, robust 367—371
Prior ignorance xiii 8 264 298 357—367 see
probability 1—3 6 7 see
Probability (mass) function, multivariate xi 128
Probability (mass) function, univariate xi 111
Probability density function see "Density function"
probability distribution 36 37 see
Probability distribution, multivariate xi 8 127—141 433—435
Probability distribution, summaries of xiv 112 113 131—133 427—435
Probability distribution, univariate xi 8 109—125 427—433
Probability distribution, utility of x xi 69—75 151—154
Probability generating function 114
Probability space 108 109 141
Probability theory, review of xi 109—141
Probability, assessment 10 150 234 235 370 375
Probability, classical (or symmetry) 3 33 99—102
Probability, degrees of belief as 33—49
Probability, frequentist 3 33 99—102
Probability, logical 3 99—102
Probability, personal 33—49 99—102
Probability, review of mathematics of xi 109—141
Probability, upper and lower 99
Probit model 219 220 382
Profile likelihood 343 455 481
Psychological research 10
Purves, R.A. 87 512
Quality assurance 374
Quantification 28—33 98 99
Quantile 112 257 370
Quantitative coherence x 22—33 83—85
Quasi-random numbers 350
Rabena, M. 302 539
Racine-Poon, A. 11 426 483 515 539 540
Radner, R. 104 533
Radon — Nikodym derivative 111 133
Raftery, A.E. 353 468 540
Rahman, M.A. 163 528
Raiffa, H. 9 10 85 91 98 103 104 417 508 526 532 540
Ramsey, F.P. 15 68 83 84 85 102 540
Ramsey, J.O. 85 368 540
Randall, C.H. 95 540
Random, characteristic function 183—185
Random, distribution function 179
Random, quantity xi 7 109—114 165—167
Random, sample 7 169 173 177 185 189 190
Random, vector xi 127—133
Randomisation 472
Rao — Blackwell theorem 464
Rao, C.R. 184 464 525 540
Rao, M.M. 258 505
Raoult, J.-R. 10 512
Rationality 4 5 13—16
Raynaud, H. 104 491
Reference analysis xiii 8 9 264 298—339 458 459
Reference analysis for an induction problem 322 323
Reference analysis for binomial and negative binomial models 315 316
Reference analysis for deviation from uniformity model 313
Reference analysis for exponential model 457
Reference analysis for infinite discrete case 338
Reference analysis for location model 320
Reference analysis for multinomial model 336 337
Reference analysis for normal correlation coefficient 337—338 363 364
Reference analysis for normal mean and standard deviation 328—330 361
Reference analysis for normal standardised mean 330—331 362 363
Reference analysis for normal variance 301 302
Reference analysis for prediction with quadratic loss 300 301
Reference analysis for product of normal means 331—333
Reference analysis for several normal means 335 364 365
Reference analysis for uniform model 311 479
Reference decisions xiii 299—302
Reference distribution and Jeffreys' prior 314 315
Reference distribution and maximum entropy 365
Reference distribution and model criticism 313
Reference distribution and ordered parametrisation 323 333 364 366
Reference distribution and strong inconsistency 365
Reference distribution and the likelihood principle 366 367
Reference distribution for hierarchical models 339
Reference distribution for prediction 339
Reference distribution in the finite case 307 308
Reference distribution, compatibility with sufficient statistics 309—310
Reference distribution, explicit form of 307 312 319
Reference distribution, given a consistent estimator 312 313
Reference distribution, given a nuisance parameter xiii 320—333
Reference distribution, independence of sample size 308 309
Reference distribution, invariance of 310 325 326
Reference distribution, multiparameter xiii 333—339
Reference distribution, one-dimensional xiii 302—320
Reference distribution, posterior 300—339 363—365 416
Reference distribution, prior 298 300—339 361 363—365 416
Reference distribution, restricted xiii 316—320
Reference distribution, under asymptotic normality 314—316 326—333
Regazzini, E. 9 89 162 483 501 540
Regression coefficient 221
Regression equation 221
Regression, inferential process for 442
Regression, multiple 221 222 383
Regression, polynomial 222
Regression, simple 222
Regression, trigonometric 222
Regressor variables 221 377
Regulation problems 483
Reichenbach, H. 100 540
Reid, N. 343 455 479 481 502 512
Relevant event see "Event"
Relevant subsets 468
Reliability 10
Remodelling xiv 377—426
Remodelling by model comparison see "Model comparison"
Remodelling by model rejection see "Model rejection"
Remodelling, critical issues xiv 418—426
Renyi, A. 77 79 91 102 158 163 540 541
Reparametrisation 189 220 235 344 345 347 348
Repeated sampling 453 454 455
Reporting beliefs 67—81 150—159 302 316 320 357 399—402 424 425
Representation theorems xii 3 7 172—207 235 236
Representation theorems for 0-1 random quantities 172—175
Representation theorems for 0-1 random vectors 176 177
Representation theorems for several sequences of 0-1 random quantities 211—215
Representation theorems under centred spherical symmetry 183—186
Representation theorems under origin invariance 187—190
Representation theorems under spherical symmetry 181—183
Representation theorems under sufficiency 191—207
Representation theorems, general form of 177—181
Residual analysis 418
Ressel, P. 236 541
Revision of beliefs x 38—45
Rfos, S. 10 99 104 516 541
Rfos, S.Jr. 104 541
Richard, J.F. 10 541
Riemannian metric 358
Rios, D. 104 371 541
Rios, M.J. 104 541
Ripley, B.D. 351 355 541
Risk function 446
Rissanen, J. 358 485 488 541
Ritter, C. 353 541
Rivadulla, A. 10 541
Robbins, H. 373 541
Robert, C.P. 9 373 374 394 465 469 495 500 508 541
Roberts, F. 10 84 104 541
Roberts, G.O. 353 354 356 541 545
Roberts, H.V. 11 98 376 425 483 542
Robinson, G.K. 468 542
Robustness xiii 5 99 160 235 239 367—371
Rodriguez, C.C. 362 542
Rolin, J.-M. 9 164 228 239 374 512 542
Rosenbluth, A.W. 533
Rosenbluth, M.N. 533
Rosenkranz, R.D. 10 542
Rossi, P.E. 417 533
Roush, F.W. 104 526
Royall, R.M. 455 542
Rubin, D.B. 10 350 353 371 374 419 515 532 533 542
Rubin, H. 263 371 417 525 542
Rueda, R. 416 417 543
Rulz-Rivas, C. 230 491
Saaty, T.L. 104 543
Sacks, J. 258 543
Saemdal, C.-E. 91 543
Sahlin, N.-E. 10 104 513
Salinetti, G. 371 532 543
Samanta, T. 289 516
Sample survey 10
Sample, mean 190
Sample, median 190
Sample, range 190
Sample, size 190
Sample, space 454
Sample, sum of squares 190
Sample, total 190
Sampling cost see "Cost of observation"
Sampling distribution 173 177 450 see parametric"
Sampling-importance-resamplin xiii 8 264 340 350—352
San Martini, A. 417 543
Sanso, B. 370 371 537 543
Sanz, R. 371 502
Savage, I.R. 9 96 543
Savage, L.J. 9 10 11 71 84 85 88 91 92 97 98 162 235 263 285 371 425 446 451 478 508 509 513 517 520 521 543 544
Savchuk, V.P. 9 544
Sawagari, Y. 10 374 544
Schader, M. 103 513
Schervish, M.J. 91 104 162 373 525 543 544
Schick, L.H. 10 519
Schlaifer, R. 9 10 85 417 539 540 543 544
Schmitt, S.A. 9 544
Schwartz, L. 463 544
Schwarz criterion 487 488
Schwarz, G. 487 544
Schweder, T. 468 540
Scientific reporting 67—77 150—157 302 320 360 399—402 424 425
Score function 6 69—75 88—89 151—157 399—409
Score function, local 72—74 153 154
Score function, logarithmic 74—81 85 91 154—159 207—209 302—339 400—407 422—424 488
Score function, proper 71—74 152 399 477
Score function, quadratic 71 72 88 89 152 397—407
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