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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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                        Gilio, A. 89 263 371 516 Gilks, W.R. 353 355 426 516 549 Gillies, D.A. 2 516 Gilliland, D.C. 373 516 Girelli-Bruni, E. 9 516 Giron, F.J. viii 99 104 373 374 419 497 500 516 Girshick, M.A. 91 446 498 517 Godambe, V.P. 10 374 517 Goel, P.K. 10 104 158 276 371 373 425 496 517 Goicoechea, A. 104 517 Goldstein, M. 11 94 163 373 426 455 517 518 Gomez, E. 417 518 Gomez-Villegas, M.A. viii 371 417 518 Good, I.J. 9 10 11 75 90 91 94 99 100 102 154 228 263 360 373 374 390 458 518 519 536 Goodman, B.C. 375 509 Goodwin, P. 375 519 Gordon, N.J. 370 519 Goutis, C. 468 519 Grandy, W.T. 10 519 546 Grayson, C.J. 10 53 519 Green, P.J. 353 356 497 Grenander, V. 374 519 Grieve, A.P. 11 426 519 540 Groenewald, P.C.N. 104 158 506 Group communication, decision making 5 8 92 102—104 166 236 237 275 424 425 Groups of transformations 362 454 460 Growth curves 220 382 Gu, C.       374 519 Gulati, C.M. 104 517 Gupta, S.S. 10 519 520 Gutierrez-Pena, E. 277 520 Guttman, I. 158 230 418 484 508 520 537 Haag, J. 235 520 Haar measure prior 362 see Hacking, I. 99 102 520 Hadley, G. 10 520 Hagen, D. 96 490 Haimes, Y. 104 500 Hald, A. 374 520 Haldane, J.B.S. 315 362 520 Hall, W.J. 228 283 502 Hall, W.K. 362 535 Halmos, P.R. 451 520 Halter, A.N. 10 520 Harris, J.E. 374 508 Harrison, P.J. 10 374 520 539 552 Harsany, J. 104 520 Hartigan, J.A. 9 99 130 163 164 250 289 359 360 362 371 455 506 520 521 Hartley, R. 10 104 513 Hasminski, R.Z. 289 523 Hastings, W.K. 356 521 Hays, W.L. 375 509 Heath, D.L. 88 90 162 172 521 Helly's theorem 126 173 213 Henrion, M. 375 534 Hens, T. 84 521 Hernandez, A. 451 500 Herstein, I.N. 91 521 Hewitt, E. 235 521 Hewlett, P.S. 219 521 Heyde, C.C. 289 521 Hierarchical model and binomial parameters 223 Hierarchical model and normal parameters 224—226 383 Hierarchical model, prior xiii 7 222—226 371—373 383 480 Highest probability density (HPD) region see "Credible region" Hildreth, C. 425 521 Hill, B.M. 11 162 227 228 250 371 373 420 496 521 522 Hill, S.D. 362 546 Hill, W.J. 417 498 Hills, S.E. 239 295 338 348 355 515 522 Hinkelmann, K. 10 522 Hinkley, D.V. 368 376 445 480 485 487 502 522 Hipp, C. 203 522 histogram 351 history 10 356 357 Hjort, N.L. 228 522 Hoadley, B. 373 522 Hodges, J.S. 10 11 104 263 419 513 514 522 Hogarth, R. 104 375 522 Holland, G.D. 2 522 Hop, J.P. 349 549 Howard, J.V. 455 518 Howson, C. 10 522 Hsu, J.S.J. 345 374 375 529 530 Hull, J. 87 91 523 Huseby, A.B. 104 523 Hutton, I. 44 535 Huzurbazar, V.S. 203 523 Hwang, J.T. 258 523 Hwang, J.T.G. 465 469 500 541 Hylland, A. 104 523 Hypergeometric distribution, model 115 172 322 428 Hypergeometric, function 338 363 Hyperparameter 224 270 271 275 339 372 Hypothesis 2 262 263 380—382 390 Hypothesis testing xiv 8 9 445 469—475 see Hypothesis testing and Lindley's paradox 394 406 407 415 416 422 Hypothesis testing in Bayesian inference 262 263 391—397 Hypothesis testing of point null hypothesis 394 406 407 414—416 Hypothesis testing, composite versus composite 392—394 396 397 Hypothesis testing, critical region 470 Hypothesis testing, inadequacies of 472—475 Hypothesis testing, likelihood ratio test 476 487—488 Hypothesis testing, minimax 472 Hypothesis testing, one-sided tests 396 397 472 Hypothesis testing, power function 470 473 Hypothesis testing, simple versus composite 392 394 Hypothesis testing, simple versus simple 392 471 Hypothesis testing, size of a test 471 Hypothesis testing, test procedure 470 Hypothesis testing, two-sided tests 473 Hypothesis testing, unbiased test 473 Hypothesis testing, uniformly most powerful test 472 473 Hypothesis, alternative 233 380 391 469 470 Hypothesis, composite 391 392 394 471—475 Hypothesis, null 233 394 414 416 469 470 Hypothesis, simple 380 391 392 394 471 475 Ibragimov, I.A. 289 523 Identifiability 239 Image analysis 5 374 implementation issues xii 263 264 Importance sampling xiii 8 264 340 348—350 Improper prior distribution 276 277 321 357—367 421—424 449 469 Improper probabilities 163 Inadmissibility 367 see Incoherence see "Coherence" Independence and dependence xi 167 168 Independence of random quantities 113 130 172—190 194—197 Independence, characterisation of 37—38 Independence, conditional 45—47 Independence, mutual 46 Independence, pairwise 28 Induction, a problem of 322 323 Inference as a decision problem 6 67—81 92 102 420 444 Inference, Bayesian 241—426 Inference, comparative 376 445 Inference, conditional and unconditional xiv 374 445 452 468 475 478 479 Inference, critical issues xiii 374 375 418—426 Inference, fiducial xiv 9 444 456—458 461 484 486 Inference, likelihood xiv 9 444 454—456 461 Inference, pivotal 458 459 461 Inference, pure problem of 6 67—81 102 Inference, statement, answer 255 Inference, structural 459—461 Inference, summaries xii 255—263 Inferential processes, Bernoulli, binomial model 248 249 270—274 276 277 279—282 436 Inferential processes, exponential model 438 Inferential processes, linear regression 442 Inferential processes, multinomial model 441 Inferential processes, multivariate normal model 441 Inferential processes, negative binomial model 437 Inferential processes, summaries xiv 436—442 Inferential processes, uniform model 438 Inferential processes, univariate normal model 439 440 Infinite exchangeability see "Exchangeability" Influential observations 418 see information 6 17 77—81 147—159 207—209 298—300 360 see Information and the exponential family xii 207—209 Information matrix see "Fisher information" Information, amount of x xi 6 77—81 Information, expected 80 91 158 159 Information, missing 304 308 324 362 Information, perfect 65 149 300 Information, theories of 10 91 92 Information, value of 65 147—149 Initial and final precision 478 479 Insufficient reason, principle of see "Bayes — Laplace postulate" Insurance 373 Interquantile range 112 Intersubjective 102—104 166 237 see Interval estimation (Bayesian) see "Credible regions" Interval estimation (non-Bayesian) xiv 445 465—469 Interval estimation (non-Bayesian), confidence limits for 465—469 Interval estimation (non-Bayesian), most selective interval 467 Interval estimation (non-Bayesian), shortest confidence interval 467 Invariance 7 454 Invariance and Laplace approximation 344 345 Invariance and noninformative priors 358 362 366 Invariance and representation theorems 181—190 204 Invariance in estimation 454 Invariance of preferences 26 Invariant prior distribution 358 362 Inverted chi-squared distribution 119 431 Inverted gamma distribution 119 431 Inverted Pareto distribution 120 432 Irony, T.Z. 11 258 374 376 491 523 Isaacs, G.L. 261 523 Isaacson, D. 371 533 Iterative quadrature see "Numerical quadrature" Iversen, G.R. 9 523 Iyengar, N.S. 10 517 Jacknife 371 Jackson, J.E. 375 523 Jackson, P.H. 10 261 523 535 Jaffray, J.Y. 99 500 James, W. 449 523 Jaynes, E.T. 10 90 227 357 363 365 366 375 451 468 523 Jefferys, W.H. 371 495 Jeffrey's rule 94 Jeffrey, R.C. 10 94 524 Jeffreys' prior, rule 314 315 357—362 see Jeffreys, B.S. 73 153 208 341 524 Jeffreys, H. 9 73 90 98 153 208 263 288 314 315 322 341 358 359 360 361 362 366 370 414 419 478 524 553 Jenkins, G.M. 250 455 492 Jennings, D.E. 419 501 Jewell, W.S. 373 524 Johnson, N.L. 114 133 524 Johnson, R.A. 289 524 Johnson, W. 418 524 Johnstone, I.M. 289 521 Joshi, V.M. 11 250 524 Justice, J.M. 10 525 Kadane, J.B. 10 11 91 98 104 130 160 162 239 243 250 341 344 371 373 375 411 472 494 505 508 525 526 543 544 549 550 551 Kagan, A.M. 184 525 Kahneman, D. 96 375 525 Kalbfleish, J.G. 455 481 484 525 Kapur, J.M. 10 525 Karlin, S. 417 525 Kashyap, R.L. 360 526 Kass, R.E. 10 289 341 348 358 361 373 417 513 526 549 Keeney, R.L. 10 91 104 526 Kelly, J.S. 104 526 Kempthome, P.J. 371 526 Kent, J.T. 374 532 Kernel density estimate 351 355 Kernel of a density 129 Kesavan, H.K. 10 525 Kestemont, M.-P 228 526 Keynes, J.M. 9 90 98 100 526 Khintchine, A.I. 235 526 Kiefer, J. 480 526 Kihlstrom, R.E. 10 499 Kim, K.H. 104 526 Kimeldorf, G.S. 228 526 Kingman, J.F.C. 106 182 527 Kirby, A.J. 353 355 516 Klein, R. 483 527 Klein, R.W. 420 527 Kleiter, G.D. 9 527 Kloek, T. 349 527 550 Klugman, S.A. 9 527 Knill-Jones, R. 95 546 Koch, G. 236 527 Kogan, N. 104 527 Kohn, R. 374 491 Kolmogorov, A.N. 485 527 Koopman, B.O. 98 527 Koopman, L.H. 203 527 Korsan, R.J. 426 527 Kotz, S. 114 133 524 Kraft, C. 90 527 Krantz, D.H. 85 90 104 527 532 Krasker, W.S. 420 527 Kuechler, U. 236 527 Kuhn, T.S. 93 527 Kullback, S. 6 76 91 208 527 Kyburg, H.E. 10 87 99 102 527 528 Lack of memory property 187 190 Lad, F. 160 163 528 Ladalla, J.N. 289 524 LaMotte, L.R. 11 528 Lane, D.A. 162 485 522 528 Laplace approximation xiii 8 264 340—345 455 Laplace's rule of succession 272 322 323 Laplace, P.S. 2 9 89 272 288 357 528 Large sample approximations see also "Asymptotic analysis" Large sample approximations to posterior distribution 285—297 314 365 Large sample approximations, comparing Bayes to classical 486 Larkey, P. 104 525 Laud, P. 228 509 Lauritzen, S.L. 95 227 236 426 507 527 528 Lavalle, I.H. 9 10 87 528 Lavine, M. 228 371 483 528 Law 10 374 Law of Large Numbers 126 Law of the iterated logarithm 127 Lawrie, T.D.V. 44 535 Le, H.       370 536 Le, N.D.       374 499 Learner, E.E. 10 263 417 528 Least favourable prior distribution 449 see Lebesgue integration, measure 111 133 141 161—163 LeCam, L. 288 485 528 529 Lecoutre, B. 10 529 Lee, P.M. 9 529 Lee, T.D. 420 545 Lee, T.M. 247 515 Lehmann, E.L. 15 68 237 238 465 529 Leibler, R.A. 76 91 527 Lejeune, M. 485 529 Lempers, F.B. 10 263 529 Length, operational definition of 82 83 Lenk, P.J. 228 529 Leonard, T. 10 228 238 345 373 374 375 407 498 529 530 Levine, R.D. 10 530 Lewis, S.M. 353 539 Ley, E. 426 530 Li, B.       341 553 Lientz, B.P. 417 508 Likelihood function 7 43 173 174 177 185 243 450 480 481 
                            
                     
                  
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