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                    Bernardo J.M., Smith A.F.M. — Bayesian Theory 
                  
                
                    
                        
                            
                                
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                                    Название:   Bayesian TheoryАвторы:   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.
Язык:  Рубрика:  Математика /Статус предметного указателя:  Готов указатель с номерами страниц ed2k:   ed2k stats Год издания:  2000Количество страниц:  586Добавлена в каталог:  12.04.2010Операции:  Положить на полку  |
	 
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                        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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