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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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                        Score function, smooth 70 151 399 Scoring rules see "Score function" Scott, D. 90 544 Scott, E.L. 480 535 Scott, W.F. 261 531 Scozzafava, R. 9 263 516 544 Sech-squared distribution see "Logistic distribution" Secretary problem 61—63 Seeber, G. 10 532 Seidenberg, A. 90 527 Seidenfeld, T. 10 90 91 104 162 373 458 472 525 527 543 544 Sellke, T. 263 475 495 Sen, A.K. 104 544 Sendra, M. 261 511 Sensitivity analysis 160 235 see Sequential, analysis 5 375 Sequential, decision problem 6 56—57 Sequential, revision of beliefs 47—49 Serfling, R.J. 295 544 Several samples xiii 211—216 381 Several Samples and Bernoulli, binomial models 211—215 216 Several Samples and multinomial models 216 Several Samples and normal models 216 Shafer, G. 84 99 102 263 394 544 Shannon, C.E. 6 80 91 102 159 544 Shao, J. 350 405 544 Sharpies, L.D. 353 355 516 Shaw, J.E.H. 347 348 349 350 420 426 544 545 Siegel, S. 91 503 Significance testing xiv 9 262 416 445 475—478 see Significance testing, inadequacies of 476 479 Significance testing, pure significance test 475 Significance testing, significance level (p-value) 471 474—478 see Significant event 27 28 Simar, L. 10 373 512 534 Simon, J.C. 10 544 Simple hypothesis see "Hypothesis" Simpson's paradox 41 42 Simpson, E.H. 42 544 Singpurwalla, N.D. 10 104 373 374 513 531 533 544 545 Singular distribution 111 Siow, A. 417 554 Sivaganesan, S. 371 545 Skene, A.M. 347 420 426 545 Skilling, J. 10 545 Slate, E.H. 348 526 Slovick, P. 96 375 525 Smith, A.F.M. vii 10 11 18 103 141 160 183 230 247 263 295 345 346 347 348 350 352 353 354 355 356 368 369 370 373 374 378 417 418 422 424 425 426 488 489 496 497 498 504 506 512 513 515 518 519 522 531 533 535 537 540 541 545 546 547 549 551 Smith, C.A.B. 99 263 394 546 Smith, C.R. 10 510 546 Smith, J.Q. 10 104 374 536 546 554 Smokier, H.E. 10 87 102 528 Smouse, E.P. 374 546 Snedecor distribution 123 124 140 432 Solomonoff, R.J. 485 546 Soubiran, C. 374 541 Soyer, R. 374 544 Spall, J.C. 10 258 362 546 Spectral analysis 10 Spezzaferri, F. 417 543 Spherical quadrature 348 Spherical symmetry 181—183 Spiegelhalter, D.J. 95 103 353 355 417 422 426 488 516 528 545 546 549 Spizzichino, F. 104 236 492 527 Splines 374 Sprott, D.A. 10 455 481 492 517 525 Spun coin, the 279—281 Squared root inverted gamma distribution 119 431 Srinivasan, C. 258 495 St. Petersburg paradox 87 Staeel von Holstein, C.-A.S. 10 375 546 Standard deviation 112 Standard events 29—32 50—52 54 Standard normal distribution 121 123 Standard Student distribution 123 Stangl, D.K. 10 497 Statistic 190 Statistical decision problem see "Decision Problem" Statistical inference see "Inference" Statistical models see "Models" Steel, M.F.J. 371 374 426 530 536 547 Steffey, D. 373 526 Stegun, I.A. 156 489 Stein's paradox 365 Stein, C. 333 361 365 367 446 449 475 523 547 Stelzer, J. 90 508 Stephens, D.A. 352 547 Stewart, L. 350 547 Stigler, S.M. 2 356 357 547 Stigum, B.P. 84 547 Stirling's formula 414 Stochastic approximation 374 Stochastic assumptions 238 239 Stochastic complexity 485 488 Stochastic simulation 264 340 348—356 Stone, M. 103 160 162 362 363 365 367 405 488 504 547 548 Stoney, D.A. 10 489 Stopping rule xii 7 247—255 367 375 Straight-line model 220 222 382 Strawderman, W.E. 465 541 Strong inconsistency 365 Strong Law of Large Numbers 126 173 182 185 188 286 288 Stroud, A.H. 348 548 Structural assumptions 238 239 Structural inference 459—461 Structured layouts xii 217 218 381 382 Studden, W.J. 160 502 510 Student distribution 122 123 136 139 239 240 329 335 369 385 416 432 459 462 469 480 see Subjective probability ix 2 3 94 99—102 Subjective probability, measurement of 31 32 85 Subjective probability, uniqueness of 35 37 41 Subjectivity ix xii 2 3 99—102 195 236 237 275 424 425 Sudderth, W.D. 88 90 162 172 485 521 528 548 Sufficiency 247—255 451 Sufficiency, parametric xii 192 193 Sufficiency, predictive xii 191—193 Sufficient statistics 7 190—207 462 Sufficient statistics for exponential family xii 197—207 Sufficient statistics in conjugate analysis 264—285 Sufficient statistics, definition of 191 192 Sufficient statistics, factorization criterion for 193 194 Sufficient statistics, minimal 197 Sugden, R.A. 160 548 Sunahara, Y. 10 374 543 Suppes, P. 11 84 90 91 104 503 527 532 548 Sure-thing principle 26 Survival analysis 5 Susarla, V. 228 548 Sweeting, T.J. 231 289 548 Symmetry 3 7 33 168—170 Symmetry, centred spherical 183—186 Symmetry, complete 169 Symmetry, spherical 181—183 t distribution see "Student distribution" Taneja, I.J. 160 536 Tanner, M.A. 353 541 549 Taylor, S.J. 106 527 Teicher, H. 178 501 Teichroew, D. 350 549 Teller, A.H. 356 533 Teller, E. 356 533 Temporal coherence 94 Test procedure see "Hypothesis testing" Test statistic 412—417 Testing hypotheses see "Hypothesis testing" Thatcher, A.R. 376 549 Thomas, A. 426 549 Thomas, H. 87 91 104 523 Thomas, L.C. 10 513 Thorburn, D. 228 549 Tiao, G.C. 9 230 258 260 360 361 367 370 419 420 498 499 537 539 549 Tibshirani, R.J. 359 371 509 549 Tierney, L. 341 344 353 356 426 526 549 Time series 5 374 Titterington, D.M. 374 549 Tiwari, R.C. 11 510 Tolerance region 484 Torgesen, E.N. 362 549 Trader, R.L. 11 549 Transformation of random quantities 111 113 130—132 246 295—297 344 347 350 358 360 Transformation, elaboration 230 231 Transitivity 24—26 84 Tribus, M. 9 10 530 549 Tritchler, D. 104 535 Truncated exponential distribution, model 200 Tsao, H.J. 373 516 Tsay, R.S. 374 533 Tsui, K.-W. 345 530 Tsutakawa, R.K. 348 512 Turing, A. 390 Turkkan, N. 160 538 Tversky, A. 10 90 96 104 375 509 525 527 531 Two-way layout 217 218 Type 1 and type 2 error probabilities       see "Hypothesis testing" Unbiased estimation 348 462—465 Uncertainty 2—5 13—16 Uncertainty precise measurement of 31—33 Uncertainty relation 21—38 106—109 Uniform distribution as prior distribution 308 320 356 357 Uniform distribution, conjugate analysis of 438 Uniform distribution, discrete 79 117 308 356 Uniform distribution, inferential process for 468 479 438 Uniform distribution, model 117 349 380 430 Uniform distribution, reference distributions for 311 438 Uniform distribution, sufficient statistics for 199 200 438 Uniformly most powerful test 472 473 Uniqueness of conditional probability measures 41 Uniqueness of probability measures 37 Urbach, P. 10 522 Utility x xi 6 16 49—75 141—154 Utility and loss functions 256 391 396 445 Utility, axioms for 90 91 Utility, bounded 49—54 Utility, canonical 50 see Utility, canonical for money 87 Utility, canonical of a probability distribution x xi 69—75 151—154 Utility, canonical, elicitation of 51 53 54 91 Utility, canonical, expected see "Expected utility" Utility, canonical, general 54 Utility, canonical, logarithmic see "Score function logarithmic" Utility, canonical, zero-one 389—395 Vaidyanathan, S. 417 526 Value of perfect information 65 66 149 van der Linde, A. viii van der Merwe, A.J. 373 549 van der Merwe, C.A. 373 549 van Dijk, H.K. 349 527 549 550 Van Ryzin, J. 228 548 van Zyl, D. 104 506 Vardeman, S. 366 533 Variance 112 113 Venn, J. 100 550 Verbraak, H.L.F. 10 550 Verdinelli, I. 160 418 546 550 Veronese, P. 279 422 501 Viertl, R. 10 550 Villegas, C. viii 362 460 500 550 von Mises, R. 100 101 550 von Neumann, J. 84 90 91 446 550 Vovk, V.G. 485 550 Vyugin V.V. 485 550 Wahba, G. 228 374 526 550 Wakefield, J.C. 355 551 Wald, A. 375 446 448 450 551 Walder, A.N. 374 532 Walker, A.M. 289 551 Wallace, C.S. 485 551 Wallace, D.L. 9 534 Wallace, M.A. 104 527 Waller, R.A. 10 532 Walley, P. 99 102 371 537 551 Wallsten, T.S. 96 551 Walsh, K. 91 548 Warren-Hicks, W.J. 373 374 553 Wasserman, L. 99 130 367 371 418 501 528 550 551 Weak law of large numbers 126 Wechsler, S. 104 236 492 551 Wedderburn, R.W.M. 488 535 Wedlin, A. 9 502 Weerahandi, S. 104 483 551 554 Wei, L.J. 228 536 Weight of evidence 390 Weighted average form of posterior means 275 276 368 Weighted average form of prediction 384 398 Weighted average of posterior distributions 281 282 387 Weighted average of prior distributions 280 282 Weiss, R.E. 418 551 Welch, B.L. 359 479 551 552 West, M. viii 10 104 230 366 370 374 375 420 483 520 528 538 539 552 Wetherill, G.B. 374 375 552 White, D.J. 10 104 513 552 Whittle, P. 162 228 552 Wichmann, D. 9 552 Wiener, N. 91 552 Wild, P. 355 516 Wilkinson, G.N. 458 553 Wilks, S.S. 133 553 Willing, R. 481 553 Wilson, J. 104 553 Wilson, R.B. 104 553 Wilson, S.P. 373 545 Winkler, R.L. 9 104 375 397 420 501 509 553 Winsten, C.B. 250 455 492 Wishart distribution 138—140 435 Wishart distribution as prior distribution 441 Witmer, J.A. 376 553 Wolfowitz, J. 480 526 Wolpert, R.L. 10 250 350 371 373 374 495 528 553 Wong, C.-M. 374 491 Wong, W.H. 341 353 549 553 Wooff, D.A. 426 553 Wright, D.E. 262 348 506 553 Wright, G. 375 519 Wrinch, D.H. 90 322 553 Wu, C.-F.       10 498 Yaglom, A.M. 10 553 Yaglom, I.M. 10 553 Ye, K.       338 367 553 554 Yilmaz, M.R. 96 554 Ylvisaker, D. 188 273 276 279 283 507 Young, K.S. 417 538 Young, S.C. 104 554 Youtz, C. 81 534 Yu, P.L.       104 554 Zabell, S.L. 94 507 Zanotti, M. 90 548 Zeckhauser, R. 104 523 Zeleny, M. 104 501 Zellner, A. 10 11 43 90 263 361 362 417 483 511 514 517 554 Zero-one, discrepancy xiv 413 414 Zero-one, utility xiii 389—395 Zidek, J.V. 11 104 362 363 374 483 499 504 506 515 551 554 Zionts, S. 104 517 
                            
                     
                  
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