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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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                        A posteriori distribution see "Posterior distribution" A priori distribution see "Prior distribution" Abramowitz, M. 156 489 Absolutely continuous distribution, multivariate 128 434 435 Absolutely continuous distribution, univariate 111 430—433 Absolutely continuous random quantity 109—111 Achcar, J.A. 345 489 Actions 5 13 15—17 Actions in bounded decision problems x 50—54 Actions in general decision problems x 54—56 Actions set of x 16 19—21 Actuarial science 9 100 373 Aczel, J. 91 489 Additive decomposition of utility 66 149 408 Adekola, A.D. 289 548 Admissibility 447—449 461 Admissibility and complete classes 448 Admissibility of Bayes rules 448 449 Admissible decision see "Admissibility" Aitchison, J. 10 99 262 483 489 Aitken, C.G.G. 10 489 Aitkin, M. 417 489 Akaike information criterion 487 488 Akaike, H. 359 367 455 487 489 490 Albert, J.H. 352 426 481 490 Aldous, D. 236 490 Allais, M. 96 97 98 490 Amaral-Turkman, M.A. 483 490 Ameen, J.R.M. 374 490 Amount of information 6 77—81 157—159 303 422 Amster, S.J. 376 490 Analysis of variance 382 Ancillarity xii 7 452 453 475 479 Andersen, E.B. 455 481 490 Anderson, T.W. 376 445 490 Angers, J.-F. 371 490 Anscombe, F.J. 10 85 295 490 Ansley, C.F. 374 491 Antoniak, C. 228 491 Aoki, M. 10 374 491 Approximations and discrepancy x xi 75—77 154—157 207—209 Approximations of a Binomial by a Poisson 76 77 Approximations of a Student by a Normal 156 Approximations of moments of a transformed beta distribution 124 125 Approximations of prior distributions 283—285 Approximations of the mean of a beta distribution 344 345 Approximations to mean and variance 113 Approximations to mean vector and covariance 132 Approximations, asymptotic see "Asymptotic analysis" Approximations, Gibbs sampling algorithm 353—355 Approximations, importance sampling xiii 8 264 340 348—350 Approximations, iterative quadrature xiii 264 346—348 Approximations, Laplace approximation xiii 8 264 340—345 455 Approximations, Markov chain Monte Carlo xiii 8 264 340 353—356 Approximations, Metropolis — Hastings algorithm 355 356 Approximations, sampling-importance-resampling xiii 8 264 340 350—352 Arimoto, S. 91 491 Arnaiz, G. 230 491 Arnold, S.F. 11 491 Arrow, K.J. 91 103 104 491 Ascending factorial function 135 Ash, R.B. 106 111 162 173 491 Asymptotic analysis xiii 8 235 264 285—297 445 463—465 480 485 486 see Asymptotic analysis, continuous xiii 287—297 Asymptotic analysis, discrete xiii 286 287 Asymptotic analysis, non-normal 296 Asymptotic normality for a ratio 297 Asymptotic normality of posterior distributions 286—297 314 365 Asymptotic normality, regularity conditions for 289—292 Asymptotic normality, under conjugate analysis 293 294 Asymptotic normality, under transformations xiii 295—297 486 Aumann, R.J. 85 104 490 491 Axiomatic approaches 5 83—91 Axiomatic approaches to degrees of belief 89 90 Axiomatic approaches to utilities 90 91 Axiomatic approaches, relevance of 94 95 see Axioms of coherence 15 16 23—28 Aykac, A. 10 491 Backward induction x 59—63 Bahadur, R.R. 451 491 Bailey, R.W. 123 491 Balch, M. 85 491 Bandemer, H. 160 491 Barlow, R.E. 11 104 172 236 374 491 492 523 Barnard, G.A. 2 95 250 270 362 376 455 458 492 Barndorff-Nielsen, O.E. 206 455 481 484 492 Barnett, V. 102 376 445 492 Barrai, I. 10 492 Bartholomew, D.J. 11 376 492 Bartlett, M. 422 493 Basu, D. 136 250 374 376 452 453 468 479 481 493 Bauwens, L. 10 493 Bayarri, M.J. viii 104 243 250 313 338 364 371 417 418 493 494 496 Bayes decision rule 448 Bayes estimate see "Estimation" Bayes factor xiii 389—395 414 417 422—424 470 476 487 488 Bayes risk 448 Bayes rules 448 Bayes test 391—397 412—417 Bayes — Laplace postulate 357 358 Bayes' theorem xii 2 4 7 162 175 180 241—255 265 269—285 305 306 340 352 368 425 451 452 454 455 480 Bayes' theorem generalised xi xiii 127 130 Bayes' theorem, finite x 2 38—40 42—45 47—49 68 77 80 89 94 Bayes, T. 1 2 89 101 102 356 357 482 494 Bayes, Thomas 1 2 Bayesian bootstrap 371 Bayesian computation vii 5 Bayesian implementation 8 263—356 Bayesian inference see "Inference Bayesian" Bayesian methods vii 5 Bayesian paradigm xiii 241—264 Bayesian reading list ix 9—11 Bayesian software 425 426 Bayesian theory vii ix 5—9 Beauchamp, T.J. 232 534 Becker, G.M. 91 494 Belief functions 95 99 Beliefs 3—9 13—16 33—49 Beliefs and actions x 13—16 Beliefs and limiting frequencies 173—175 177 179 181 Beliefs and models xi xiii 165—167 Beliefs and probabilities x 33—49 Beliefs, conditional x 38—49 Beliefs, finite representation of x 33—38 Beliefs, general representation of xi 105—109 Beliefs, reporting of x xi 67—81 150—157 302 320 360 Beliefs, revision of x 38—49 127—130 Beliefs, sequential revision of x 47—49 56—67 Bellman, R.E. 61 494 Berger, J.O. viii 9 10 11 102 250 258 263 302 306 307 333 334 337 338 362 366 370 371 373 375 394 417 423 449 475 479 490 493 494 495 496 506 519 520 536 554 Berger, R.L. 104 376 445 475 495 500 Berk, R.H. 287 495 Berliner, L.M. 228 371 374 494 495 496 Bermudez, J.D. 71 232 289 419 496 497 Bernardo, J.M. 9 10 11 18 71 92 141 156 232 302 305 306 307 313 323 333 334 337 338 362 365 366 373 374 394 417 419 422 468 481 483 494 495 496 497 Bernoulli distribution and exchangeability xi 172—175 211—215 Bernoulli distribution, "biased" stopping rule for       251 252 Bernoulli distribution, asymptotic analysis for 294 296 Bernoulli distribution, conjugate analysis of 270—272 436 Bernoulli distribution, conjugate family for 267 270 Bernoulli distribution, inferential process for 248 249 270—274 276 277 279—282 436 Bernoulli distribution, model 115 428 Bernoulli distribution, reference distributions for 315 316 337 436 Bernoulli distribution, sufficient statistics for 195 196 436 Bernoulli, D. 87 497 Bernoulli, J. 89 101 497 Berry, D.A. 10 160 376 495 497 536 Besag, J. 353 356 374 497 Bessant, R.G. 44 535 Best, N.G. 353 355 516 Beta distribution 116 117 124 125 134 135 430 Beta distribution as prior distribution 267 270—273 344 Beta distribution, mixtures of 279—281 Beta-binomial distribution see "Binomial-beta distribution" Betting see "Monetary Bets" Bias 360 462—465 Bickel, P.J. 455 463 497 Bilateral Pareto distribution 141 434 Binder, S. 373 497 Binomial distribution see also "Bernoulli distribution" Binomial distribution, asymptotic analysis for 294 296 Binomial distribution, conjugate analysis of 270—272 Binomial distribution, conjugate family for 267 271 Binomial distribution, inferential process for 248 249 270—274 279—282 414 Binomial distribution, model 115 134 172—175 211—215 428 Binomial distribution, reference distributions for 315 316 337 Binomial distribution, sufficient statistics for 195 196 Binomial-beta distribution 117 272 428 Bioassay 219 220 382 Biostatistics 9 Birnbaum, A. 11 250 455 456 497 Bjornstad, J.F. 455 485 498 Blackwell, D. 91 103 159 356 463 464 498 Blyth, C.R. 42 498 Boos, D.D. 455 534 Booth, N.B. 374 498 Bootstrap 371 see bootstrap" Bordley, R.F. 96 498 Borel, E. 89 498 Borelset 110 127 Borovcnik, M. 9 498 Bowen, K.C. 10 104 552 Box, G.E.P. 9 10 44 92 93 230 231 258 260 263 360 361 367 370 376 413 417 419 498 499 549 Boyer, J.E.Jr. 373 516 Boyer, M. 10 499 Brant, R. 418 500 Breslow, N. 11 499 Bretthorst, G.L. 10 499 Bridgman, P.W. 82 499 Brier, G.W. 71 499 Brillinger, D.R. 458 499 Broemeling, L.D. 10 499 Brown, L.D. 10 206 258 499 Brown, P.J. 10 373 374 499 Brown, R.V. 100 104 499 531 Brown, S.J. 420 527 Brumat, C. 10 491 Brunk, H.D. 162 499 Buehler, R.J. 88 154 468 469 499 Bunn,D.J. 104 499 Butler, R.W. 455 485 499 Calibration 373 482 Called-off bets 87—89 Campling, G.E.G. 374 552 Cano, J.A. 371 394 451 500 534 Canonical conjugate analysis 269—279 Carlin, B.P. 355 374 500 Carlin, J.B. 371 500 Carnap, R. 90 100 500 Caro, E. 104 500 Casella, G. 353 376 445 468 469 475 500 519 532 Cauchy distribution 123 349 Cauchy distribution, location parameter estimation 451 Central limit theorem 126 Centred spherical symmetry 183—186 Chaloner, K. 160 418 500 Chan, K.S. 353 500 Chang, H. 418 419 420 515 Chang, T. 362 500 Chankong, V. 104 500 Chao, M.T. 289 500 Characteristic function 114 126 183—186 203 Chateaneuf, A. 99 500 Chen, C.F. 289 501 Chernoff, H. 10 91 160 475 501 Chi-squared distribution 118 121 123 124 138 330 361 414 431 459 487 Choice of experiments see "Design of experiments" Chow, Y.S. 178 501 Christ, D.E. 261 523 Chuang, D.T. 371 525 Chuaqui, R. 90 501 Cifarelli, D.M. 9 10 11 483 501 Clarke, B. 367 501 Clarke, R.D. 100 501 Claroti, C.A. 10 501 Classical decision theory xiv 444—449 461 Classification 373 407 408 483 Clayton, D.G. 353 355 516 Clayton, M.K. 104 419 501 516 Clemen, R.T. 104 501 Closed under sampling 270 281 see Cluster analysis 418 Cochrane, J.L. 104 501 Coding theory 358 see Coherence x 23—33 38—45 83—91 94—99 195 see Coherence and preferences x 23—28 Coherence and quantification x 28—33 83—85 Coherence, temporal 94 Coletti,G. 10 492 Collier, R.O. 10 412 Combining evidence 103—104 Communication 92 102—104 166 236 237 Comparability of consequences 23 24 Comparability of events 33 Comparative inference xiv 376 443—488 Compatibility of probability and degrees of belief 35 40 Complete probability measures 108 Complete symmetry 169 Composite hypothesis see "Hypothesis" Computer software 425 426 Conditional, beliefs see "Beliefs" Conditional, density function 128—131 166 172—226 242—247 353—355 Conditional, expectation 51 52 Conditional, independence see "Independence" Conditional, inference xiv 374 445 452 468 475 478 479 Conditional, likelihood 48 Conditional, mass function 128—130 Conditional, preference 22 85 Conditional, probability 38—49 Conditional, uncertainty relation 22 38—40 Confidence interval, region 359 445 453 465—469 478 see Confidence level, coefficient 466 Confirmation theory 95 Conjugate analysis xiii 8 9 264—285 see Conjugate prior family of distributions, approximation with 279—285 Conjugate prior family of distributions, canonical form of 269 Conjugate prior family of distributions, convex combination (mixtures) of 282 283 Conjugate prior family of distributions, definition of 265 266 Conjugate prior family of distributions, for regular exponential models 266—279 Conjugate prior family of distributions, limiting form of 276 362 Conjugate prior family of distributions, logarithmic divergence between 278 Conlisk, J. 87 501 Consequences 16 17 19—21 Consequences, bounded set of 49—54 Consequences, extreme 49—54 Consequences, reference 54—56 Consistency of preferences 26 Consistent sequence of statistics, estimates 312 320 326 353 405 Consonni, G. 279 422 501 Constrained parameters 246 247 Contingency table 41 216 374 414 Continuity of uncertainty relation 107 Control problems, theory 9 374 Convergence xi 125—127 Convergence in distribution 125 126 Convergence in expected utility 142—147 Convergence in mean square 125 126 Convergence in probability 125 126 Convergence, almost surely 125 126 352 Cook, R.D. 418 551 
                            
                     
     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