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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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                        Likelihood function, approximation for large samples 485 486 Likelihood function, conditioned 48 Likelihood function, integrated 245 390 470 Likelihood inference xiv 9 444 454—456 461 Likelihood principle 249 250 454 Likelihood principle and noninformative priors 367 Likelihood principle and stopping rules 250—255 Likelihood principle, derivation of 249 250 Likelihood principle, implies sufficiency 455 Likelihood principle, satisfied by Bayesian analysis 249 Likelihood principle, violation of 463 Likelihood ratio 49 392 455 470 476 487 Limit theorems xi 125—127 Limiting frequency 173 174 177 179 450—454 Lindgren, B.W. 10 530 Lindley's paradox see "Hypothesis testing" Lindley, D.V. viii 9 10 11 42 62 87 88 90 91 103 104 158 159 160 261 263 272 289 338 345 359 364 367 373 374 375 394 417 449 455 457 460 472 484 486 496 497 499 501 504 530 531 537 Lindman, H. 11 263 371 425 509 Linear models 5 10 221 222 442 see Linear theory (based on expectation operator) 162 163 Linear transformation of utilities 55 Linnik, Y.V. 184 525 Liseo, B. 371 481 531 532 Little, R.J.A. 374 532 Lo, A.Y.       228 371 374 508 532 Location-scale parameters 320 362 379 380 415 458 Logarithmic divergence 76 91 278 279 286 287 358 402 416 476 Logistic distribution 122 239 240 349 433 Logistic model 220 382 Logit model 219 220 382 Lorimer, A.R. 44 535 Loss functions 256—263 445—449 461 Loss functions for inference problems 256—263 Loss functions from utility functions 256 391 396 445 Loss functions, absolute value 257 Loss functions, linear 257 396 397 Loss functions, logarithmic divergence 279 Loss functions, quadratic 85 88 257 300 301 397 401 406 Loss functions, standardised quadratic 301 Loss functions, zero-one 257 405 Lottery see "Option" Lottery, canonical 85 Louter, A.S. 349 549 Luce, R.D 11 85 90 91 96 103 104 527 532 Lusted, L.B. 10 532 Lwin, T. 373 532 Maatta, J. 468 532 Machina, M. 91 96 532 Maekelaeinen, T. 373 499 Mahalanobis distance 416 Main, P. 370 371 518 532 Makov, U.E. 373 374 515 532 549 Malitz, J. 90 501 Mardia, K.V. 374 532 Marginal distribution 128 166 Marginalisation paradoxes 363 364 479—481 Marginalisation procedures xiv 128 445 Marinell, G. 10 532 Maritz, J.S. 373 532 Markov chain Monte Carlo xiii 8 264 340 353—356 Marriage problem 61—63 Marriott, J.M. 348 426 532 533 Marschak, J. 91 104 494 533 Martin, J. 371 541 Martin, J.J. 10 533 Martinez, L. 419 516 Martz, H.F. 10 533 Maryak, J.L. 258 546 Masreliez, J.L. 370 533 Mathematics, the role of xi 30 31 49 50 82 85 105 106 141 142 160—164 170 226—229 Matheson, J.E. 10 375 546 Mathiasen, P.E. 484 533 Maximisation of expected utility 52 56 90 91 146 147 256 386 388 Maximum entropy, procedures 10 209 366 Maximum likelihood estimate 288 461 465 Maximum likelihood estimate, asymptotic distribution of 485 Mazloum, R. 160 533 McCardle, K.F. 104 535 McCarthy, J. 91 533 McClintock, C.G. 91 494 McCulloch, R.E. 232 367 374 417 418 515 533 McDunnough, P. 289 512 McKillop, J.H. 44 535 McNeil, A.J. 353 355 516 Mean 112 131 357 258 461 see Mean squared error 462—465 Measure theory 111 133 141 161—163 177 Median 112 257 258 461 Medical diagnosis 44 45 Meeden,G. 160 366 371 533 Meinhold, R. 374 533 Mendel, M.B. 236 491 533 Mendoza, M. viii 295 307 362 495 533 Meng X.-L. 374 533 Merkhofer, M.W. 375 533 Meta-analysis 374 Metropolis — Hastings algorithm 355 356 Metropolis, N. 356 533 Meyer, D.L. 10 533 Migon, H.S. 374 512 552 Miller, M. 374 519 Mills, J.A. 374 534 Milnor, J. 91 521 Minimax principle, procedures 360 449 461 472 Missing data 374 Missing information 304 308 324 362 Mitchell, T.J. 160 232 534 Mixtures see "Representation theorems" Mixtures, finite 279—283 374 462 Mockus, J. 10 534 MODE 112 257 258 461 Model comparison and Bayes factors xiii 390—394 405 414 417 422—424 Model comparison and covariate selection xiii 407—409 Model comparison as a decision problem xiii 386—409 Model comparison perspectives, closed view 384 Model comparison perspectives, completed view 385 Model comparison perspectives, open view 385 Model comparison, approximation by cross validation xiii 403—407 409 420—424 Model comparison, general utilities for xiii 395—402 Model comparison, perspectives on xiii 383—385 Model comparison, zero-one utilities for xiii 389—395 Model rejection, discrepancy measures for xiv 412—417 Model rejection, through model comparison xiv 409—412 Modelling xi 7 165—240 Modelling, critical issues xii 237—240 Modelling, scientific 237 238 Modelling, technological 237 238 Modelling,and exchangeability 167—181 Modelling,and invariance 181—190 Modelling,and partial exchangeability 209—222 Modelling,and remodelling xiv 377—426 Modelling,and sufficient statistics 191—207 Models 7 114 Models and invariance xii 181—190 Models, choice of xiv 8 377—409 419 420 445 486—488 Models, comparison of xiii 377—409 483 Models, criticism of 419 420 483 Models, elaboration of xii 229—232 Models, empirical 237 238 Models, explanatory 237 238 Models, nonparametric xii 228 Models, parametric xii 7 172—234 242—255 380—383 Models, predictive 165—167 243 244 Models, ranges of xiii 8 277—283 Models, rejection of xiv 409—417 Models, role of 237 238 Models, simplification of xii 233 234 Mohammad-Djafari, A. 10 534 Moment-generating function 114 Moments 112 113 131 132 Monahan, J.E 455 534 Monetary bets 86—88 162 Monotone continuity of uncertainty relation 107 Monotonicity of uncertainty relation 27 Monte Carlo methods see "Stochastic simulation" Moore, P.G. 87 91 523 Morales, D. 160 536 Morales, J.A. 10 239 534 Morcillo, C. 419 516 Moreno, E. viii 371 394 451 500 534 Morgan, M.G. 375 534 Morgenstern, O. 84 90 91 446 550 Morris, C.N. 206 343 344 373 509 534 Morris, M.D. 160 534 Morris, P.A. 104 534 Morris, W.T. 10 534 Mortera,J. 104 371 374 394 495 505 534 Moses, L.E. 10 91 501 Mosteller, F. 9 81 534 Mouchart, M. 9 10 130 164 239 373 374 420 512 534 Mueller, P. 374 552 Muirhead, C.R. 230 535 Mukerjee, R. 324 359 516 535 Muliere, P. 9 501 Multinomial distribution and exchangeability xi 176 177 Multinomial distribution, conjugate analysis of 441 Multinomial distribution, conjugate family for 441 Multinomial distribution, inferential process for 441 Multinomial distribution, model 133 134 176 177 216 433 Multinomial distribution, reference distributions for 336 441 Multinomial—Dirichlet distribution 135 136 433 Multinomial—Dirichlet distribution as predictive distribution 441 Multiple regression 221 222 383 442 Multivariate analysis 5 10 374 Multivariate distributions 133—141 433—435 Multivariate normal distribution and exchangeability xi 185 186 Multivariate normal distribution as approximation to posterior distribution 286—297 314 365 Multivariate normal distribution as prior distribution 441 442 Multivariate normal distribution, conjugate analysis of 441 Multivariate normal distribution, conjugate family for 441 Multivariate normal distribution, inferential process for 441 449 Multivariate normal distribution, model 136—138 140 365 434 Multivariate normal distribution, reference distributions for 441 Multivariate normal distribution, sufficient statistics for 441 Multivariate normal-gamma distribution 140 435 Multivariate normal-gamma distribution as prior distribution 442 Multivariate normal-Wishart distribution 140 435 Multivariate normal-Wishart distribution as prior distribution 441 Multivariate Student distribution 139 140 435 Multivariate Student distribution as marginal posterior distribution 441 Multivariate Student distribution in linear model 442 Munoz, J. viii Murphy, A.H. 71 535 Murray, R.G. 44 535 Mutual independence 46 Myerson, R.B. 89 535 Nakamizo, T. 10 374 543 Nakamura, Y. 99 535 Narens, L. 84 90 532 535 Nau, R.F. 104 371 535 Naylor, J.C. 346 347 426 533 535 545 Nazaret, W.A. 371 537 Negative-binomial distribution 116 119 429 Negative-binomial distribution, conjugate analysis of 437 Negative-binomial distribution, conjugate family for 437 Negative-binomial distribution, inferential process for 437 Negative-binomial distribution, reference distributions for 437 Negative-binomial distribution, sufficient statistics for 437 Negative-binomial-beta distribution 118 429 Neighbourhood of distributions 370 Nelder, J.A. 488 535 Newman, J.R. 104 509 Neyman factorisation criterion 193—195 Neyman — Pearson lemma 471 472 Neyman, J. 195 446 450 471 480 535 Nicolau, A. 359 535 No-data problems 446 Non-Bayesian theories, alternative approaches xiv 445—460 Non-Bayesian theories, hypothesis testing xiv 469—475 Non-Bayesian theories, interval estimation xiv 465—469 Non-Bayesian theories, point estimation xiv 460—465 Non-Bayesian theories, significance testing xiv 475—478 Non-central chi-squared distribution 121 431 Non-informative prior 277 298 314 357—367 see Non-informative prior, invariant prior 358 361 362 366 Non-informative prior, Jeffreys' prior 314 315 357—362 Nonparametric models, inference xii 5 228 Normal distribution and exchangeability xii 181—185 Normal distribution as approximation to posterior distribution 286—297 314 365 Normal distribution as maximum entropy choice 209 Normal distribution as prior distribution 253 300 Normal distribution, "biased" stopping rule for       253—255 Normal distribution, conjugate analysis of 274 439 440 Normal distribution, conjugate family for 268 439 440 Normal distribution, inferential process for 253—255 297 361—365 369 394 396 397 401 402 406 407 415 416 439 440 446 453 473 Normal distribution, model 7 121 123 136 155—157 181—185 196 216 432 459 463 464 478 480 Normal distribution, reference distributions for 328—333 439 440 Normal distribution, sufficient statistics for 196 199 439 440 462 Normal-gamma distribution 136 434 Normal-gamma distribution as prior distribution 268 Normand, S.-L. 104 535 Novick, M.R. 10 42 261 362 368 523 531 535 540 Nuisance parameter xiv 245 445 479—481 Numerical approximations xiii 339—356 see Numerical quadrature xiii 8 264 346—348 O'Hagan, A. 9 10 230 348 370 371 423 495 510 535 536 Objectivity xii 2 3 99—102 236 237 275 298 424 425 Observables xii 7 241—247 Occam's razor 476 Odds 49 357 390 391 Oil wildcatters 53 54 Oliver, R.M. 10 536 Operational perspective x 18 22 51 81—83 85 87 90 94 99 100 102 161 195 235 243 298 Opportunity loss 65 149 Optimal stopping 59—63 Optimisation 10 options 18 19 Options, finite 23—33 Options, generalised xi 141—149 Options, standard 29—33 Ord, K. 407 530 Ordered parametrisation 323 333 364 367 Ordering see "Preference relation" Origin invariance 187—191 Osiewalski, J. 371 536 Osteyee, D.D.B. 10 536 Outlier 229 230 240 370 Overfitting 420 421 p-values 474—478 Pack, D.J. 11 536 Padgett, W.J. 228 536 Page, A.N. 91 536 PARAMETER 7 173—177 179—190 192—197 220 235 see Parameter as label of distribution 114—125 133—141 Parameter of conjugate family 265 266 Parameter of interest 245 Parameter, equality 233 234 Parameter, nuisance 245 445 479—481 Parametric, inference 243—247 Parametric, model xii 228 229 Parametric, sufficiency xii 192 193 Pardo, L. 160 536 Parenti, G. 10 536 Pareto distribution 120 141 432 Pareto distribution as prior distribution 438 Parmigiani, G. 160 536 Partial exchangeability xii 7 168—170 208—222 Pascal distribution see "Geometric distribution" Pathak, P.K. 10 516 Pattern recognition 10 
                            
                     
                  
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