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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
Cooke, R.M. 10 501
Cornfield, J. 11 88 361 468 502 514
Correlation 132 231 232
Correlation, inference for 337 338 363 364
Correlation, reference distributions for 337 338 363 364
Cost of observation, experiment 66 67 149 408 409
Countable additivity xi 6 106—109 161 162
Covariance (matrix) 132
Covariates and partial exchangeability xii 7 209—211 219—222
Covariates elaboration 232 234
Covariates selection of xiii 407—409
Coverage probability 365
Cowell, R.G. 426 502 546
Cox, D.D. 374 502
Cox, D.R. 68 231 237 238 343 368 376 445 455 479 480 481 484 487 498 502
Cox, R.T. 90 502
Credible regions 8 259—262 466
Credible regions lack of invariance of HPD 262
Credible regions loss function for 259
Credible regions size of 259
Credible regions, coincidence with confidence sets 359 468 469
Credible regions, highest posterior density (HPD) 260—262 395 453 477 484 486
Credible regions, intervals 259
Critical value 412 413
Cross-validation xiii 8 403—407 409 420—424
Crosse, J. 375 552
Crowder, M.J. 289 502
Csiszar, I. 366 502
Cuevas, A. 371 502
Cyert, R.M. 10 502
D-optimality 159
Daboni, L. 9 502
Dalal, S. 228 283 502
Dale, A.I. 2 10 502
Darmois, G. 203 502
DasGupta, A. 10 160 262 495 502
DATA 2 63 147
Data, "speaking for themselves" 276 298 357
Data, expected information from 78 158
Data, expected utility of 78 157
Data, expected value of 65 148
Data, reduction 190 191
Data, structures xii 209—226
Data, transformation 230 231
Davis, W.W. 350 547
Davison, A.C. 455 503
Davison, D. 91 503
Dawid, A.P. 10 11 47 93 162 183 230 236 250 279 289 362 363 371 373 374 460 481 485 488 496 503 504 545 548
de Finetti, B. vii 2 3 9 10 11 71 77 86 87 88 89 101 102 106 109 110 162 163 172 212 230 235 242 375 483 504 505
de la Horra, J. viii 258 371 463 506
De Morgan, A. 89 506
de Vos, A.F. 423
De Waal, D.J. 104 158 506
Dean, G.W. 10 520
Debreu, G. 91 504
Decision 3—9 13—22
Decision analysis 9 10
Decision criterion 52 56 146
Decision function 141—145
Decision problem x 16—22
Decision problem, basic elements of x 16—18 255 256
Decision problem, bounded x 50—54
Decision problem, formal representation of x 18—22
Decision problem, general x 54—56
Decision problem, sequential x 56—67
Decision rule 446
Decision theory 5
Decision tree 16 17 58 59 63 147 148 386—388 408 410 411
Decision, classical theory of xiv 9 444—449
Deely, J.J. 160 373 504 528 531
Degrees of belief 33—49 see
Degrees of belief and monetary bets 86—88
Degrees of belief and scoring rules 88 89
Degrees of belief, axiomatic approaches to 89 90
DeGroot, M.H. viii 9 10 11 62 91 102 104 133 158 160 243 250 258 263 276 289 362 373 375 376 397 417 418 445 449 493 494 497 502 505 508 517
Delampady, M. 263 371 394 417 475 495 506
Dellaportas, P. 348 355 506
Demoment, G. 10 534
Dempster, A.P. 99 371 419 500 506
Density estimation 482
Density function see also "Conditional"
Density function, joint 128 166
Density function, marginal 128 166
Density function, multivariate 128
Density function, univariate 111
DeRobertis, L. 99 371 506
Descriptive theory 4 23 32 95—98
Design matrix 221
Design of experiments x 5 63—67 147—149 159—160
Desu, A. 483 514
Deviation from uniformity model 313
Devroye, L. 355 506
Dey, D.K. 359 371 418 419 420 506 514 515 535
Di Bacco, M. 10 492
Diaconis, P. viii 94 188 204 206 207 226 227 236 273 276 279 283 348 463 506 507 512
Diagnostic functions 418 419
Dickey, J.M. 11 103 123 163 228 263 283 375 378 411 417 424 425 507 508 513 528
Diebolt, J. 374 508
Digamma function 156
Dirichlet distribution 134—135 434
Dirichlet distribution as prior distribution 441
Discrepancy of an approximation x xi 76 77 156 157 207—209 298
Discrepancy, measures for model rejection 412—417
Discrete distribution, multivariate 128 433
Discrete distribution, univariate 110 428 429
Discrete random quantity 109—111
Discrimination 373
Distribution function, multivariate 128
Distribution function, univariate 110
Doksum, K.A. 228 371 508
Domfnguez, J.I. 104 500
Dominance 447
Domotor, Z. 90 508
Double-exponential distribution 369 379 380
Dransfield, M. 347 426 545
Draper, N.R. 158 508
Dreze, J.H. 239 508
Dubins, L.E. 9 104 162 498 508
Duckstein, L. 104 517
DuMouchel, W. 374 508
Duncan, G. 160 508
Duncan, L.R. 10 508
Dunsmore, I.R. 10 373 483 489 490 508
Durbin, J. 250 475 508 509
Dutch book 86 88 95
Dykstra, R.L. 228 509
Dynamic programming see "Backward induction"
Dynkin, E.B. 235 509
Earman, J. 2 509
Eaton, M.L. 89 227 362 367 507 509
Eaves, D.M. 362 422 500 509
Econometrics 10 374
Economics 10
Eddy, W.F. 419 514
Educational research 10
Edwards, A W.F. 455 509
Edwards, W.L. 10 11 91 103 104 263 371 375 425 509
Effects (main, interaction) 218 234 382
Efficient score function 368 464
Efron, B. 365 371 373 458 481 509
Eichhorn, W. 37 509
El-Krunz, S.M. 160 510
Eliashberg, J. 104 509
Ellsberg, D. 96 98 510
Empirical Bayes xiii 226 371—373
Empirical distribution function 177—181 228 229 351
entropy 77 79 see
Epstein, E.S. 71 535
Ergodic average 353
Erickson, G.J. 10 510 546
Ericson, W.A. 11 373 374 510
Erlang distribution 118
Errors of type 1 and 2 471
Escobar, M.D. 374 552
Essentially bounded functions 142—144
Estimation see "Interval Estimation" and "Point Estimation"
Ethically neutral event 83 84
Events x 16—18
Events, real-world 19
Events, relevant 18—22 92 95
Events, significant 27 28
Events, standard 29—32 50—52 54
Exchangeability xi 3 101 167—181 223—226 403 425
Exchangeability, extensibility of 171 226 227
Exchangeability, finite 169 170 226 227 356 357
Exchangeability, infinite 171 172—226 357
Exchangeability, partial xii 7 168—170 209—222 381
Exchangeability, role of 7
Exchangeability, unrestricted 211—216
Exchangeability,and independence 167 168
Exchangeability,and invariance 181—190
Exchangeability,and sufficient statistics 191—207
Exchangeability,of parameters 222—226 372
Exchangeable, binomial parameters 223
Exchangeable, normal mean parameters 224—226
Expectation see also "Mean" and "Conditional"
Expectation of a random quantity 112
Expectation of a random vector 131 132
Expected, information 80 91 158 159
Expected, loss 75 76 154 155
Expected, utility 6 51—81 84 90 91 141—147 155—157 299—302
Experiment see also "Design of experiments"
Experiment, expected information from 80 158 159 299 300
Experiment, expected value of 65—67 148 299 300
Expert system 426
Exponential distribution and exchangeability xii 187—189
Exponential distribution as maximum entropy choice 209
Exponential distribution, conjugate analysis of 438
Exponential distribution, conjugate family for 438
Exponential distribution, inferential process for 438
Exponential distribution, model 7 118 187—189 199 430
Exponential distribution, reference distributions for 438
Exponential distribution, sufficient statistics for 197 438
Exponential family of distributions 7 197—209
Exponential family of distributions and exchangeability xii 204—207
Exponential family of distributions and maximum entropy 207—209
Exponential family of distributions as an approximation 207—209
Exponential family of distributions, canonical form of 202—203
Exponential family of distributions, conjugate analysis of 269—279
Exponential family of distributions, conjugate family for 265—279
Exponential family of distributions, first two moments of 203
Exponential family of distributions, inferential process for 273—276
Exponential family of distributions, information measures and xii 207—209
Exponential family of distributions, k-parameter 201 202
Exponential family of distributions, non-regular 198—200
Exponential family of distributions, one-parameter 198—200
Exponential family of distributions, regular 198 199
Exponential family of distributions, sufficient statistics for 197—207
Extreme consequences 49—54
F distribution see "Snedecor distribution"
Fan, T.H. 371 495
Fang, B.Q. 373 504
Farrell, R.H. 258 263 510
Faulkenberry, G.D. 485 529
Fearn, T. 10 510
Feddersen, A.P. 469 499
Fedorov, V.V. 159 510
Feller, W. 46 510
Fellner, W. 10 510
Felsenstein, K. 160 417 510
Ferguson, T.S. 11 62 102 228 446 463 510
Fernandez, C. 371 506
Ferrandiz, J.R. 18 141 261 365 416 417 497 510 511
Fiducial inference xiv 9 444 456—458 461 484 486
Fieller — Creasy problem 468
Fieller, E.C. 458 511
Fienberg, S.E. 10 104 505 511
Final precision see "Initial and final precision"
Fine, T.L. 56 98 99 102 511 551
Finite additivity xii 16 36 40 105 106 108 161 162
Finite decision problems 16
Finite exchangeability 169 170 226 227 356 357
Finite horizon 59
Finite population sampling 374
Fishburn, P.C. 10 11 83 84 85 90 91 102 103 104 491 511
Fisher distribution see "Snedecor distribution"
Fisher information (matrix), expected 288 314 329 331 333 335 336 361
Fisher information (matrix), observed 288
Fisher, R.A. 68 195 314 338 420 424 450 451 457 460 511
Flatland paradox 365
Fliihler, H. 11 426 540
Florens, J.-P. 9 10 164 239 362 374 420 512
Flournoy, N. 348 512
Forecasting 10 374
Forensic science 10
Fougere, P.T. 10 512
Foulis, D.J. 95 540
Foundations x 10 13—104
Foundations, and coherence x 23—33 38—45 83—91 94—99
Foundations, axiomatic basis of x 5 15 16 23 83—91 94 95 444
Foundations, critical issues x xi 92—104
Foundations, theories x 83—92
Fractiles see "Quantiles"
Frame of discourse 18 92—94
Fraser, D.A.S. 250 289 455 459 460 481 512
Freedman, D.A. 87 182 204 206 207 226 227 235 236 289 463 507 512 513
Freeman, P.R. 10 62 103 230 425 485 508 513 551
French, S. 5 10 90 104 375 513 541
frequency see "Limiting frequency"
Frequentist procedures xiv 9 371 444 449—454 461
Friedman, M. 91 513
Fu, J.C. 289 513
Fuzzy logic 95
Gaerdenfors, P. 10 104 513
gambling see "Monetary bets"
Game theory 5 88 104 360
Gamerman, D. 374 513
Gamma distribution 118 123 124 136 138 140 313 330 430
Gamma distribution as a prior distribution 267 268 274 301 302
Gamma function 116
Gamma-gamma distribution 120 430
Gamma-gamma distribution as predictive distribution 438
Gamma-Poisson distribution see "Poisson-Gamma distribution"
Garthwaite, P.H. 375 513
Gaskins, R. 228 519
Gathercole, R.B. 374 546
Gatsonis, C.A. 10 89 513
Gaul, W. 103 513
Gauss — Hermite quadrature 264 346
Geisser, S. 10 11 90 316 322 361 362 373 405 418 419 483 485 501 513 514 524
Gelfand, A.E. vii 247 350 353 355 418 419 420 483 500 514 515 545 551
Gelman, A. 353 515
Geman, D. 354 374 515
Geman, S. 354 374 515
Generalised gamma function 138
Genest, C. 11 104 515
Geometric distribution and exchangeability xi 189 190
Geometric distribution, conjugate analysis of 437
Geometric distribution, inferential process for 437
Geometric distribution, model 116 189 190
Geometric distribution, reference distributions for 437
Geometric distribution, sufficient statistics for 437
George, E.I. 232 353 367 373 500 515
Geweke, J. 349 515
Geyer, C.J. 353 515
Ghosal, S. 289 516
Ghosh, J.K. 289 324 455 497 516
Ghosh, M. 10 11 258 373 516
Gibbs sampling algorithm 353—355
Gilardoni, G.L. 104 516
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