Àâòîðèçàöèÿ
Ïîèñê ïî óêàçàòåëÿì
Walley P. — Statistical reasoning with imprecise probabilities
Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå Íàøëè îïå÷àòêó?
Íàçâàíèå: Statistical reasoning with imprecise probabilitiesÀâòîð: Walley P. Àííîòàöèÿ: This text presents a theory of probabilistic reasoning, statistical inference and decision. The book is concerned with the problems of reasoning under conditions of uncertainty, partial information and ignorance. It is argued that, in order to give appropriate weight to both ignorance and uncertainty, imprecise probabilities need to be assessed. The imprecision can be modelled mathematically by upper and lower probabilities or (more generally) upper and lower previsions. The degree of imprecision can reflect both the amount of information on which probabilities are based and the extent of conflict between different types of information. The book develops mathematical methods for reasoning using imprecise probabilities. These include methods for assessing probabilities, modifying the assessments to achieve coherence, updating them to take account of new information, and combining them to calculate other probabilities, draw conclusions and make decisions. The methods are extended in the second half of the book to construct a general theory of conditional probability and statistical inference. The mathematical theory is based on simple and compelling principles of avoiding sure loss, coherence and natural extension. Careful attention is given to the philosophical foundations, interpretation and justification of the theory. It is compared with alternate theories of inference, including Bayesian theories (which require all probability assesments to be precise), Bayesian sensitivity analysis, the Neyman-Pearson theory of confidence intervals, the Dempster-Shafer theory of belief functions and the theory of fuzzy sets. The theory is applicable to a wide range of disciplines including statistics, decision theory, economics, psychology, philosophy of science, management science, operations research, engineering and artificial intelligence. (References are given to related work in these fields). In fact, the theory has important implications for any field in which the problems of uncertainty and limited information are taken seriously. This book should be of interest to researchers in statistics and those in related disciplines.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1991Êîëè÷åñòâî ñòðàíèö: 706Äîáàâëåíà â êàòàëîã: 10.12.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Lebesgue measure (on unit interval), inner and outer 98—99 131—32 136 37 149—50 325 327 Lebesgue measure (on unit interval), non-measurable sets 149—50 Lebesgue measure (on unit interval), translation-invariant extensions 144—45 Lehman, R.S. 494 Lehmann, E.L. 501 569 570 571 573 Leibler, R.A. 523 Lemmer, J.F. 490 Levi, I. 34 44 48 238 478 480 481 482 483 487 488 490 496 499 507 519 520 530 532 536 537 543 545 547 555 557 562 563 564 592 Levine, R.D. 540 Lewis, D. 563 Lichtenstein, S. 480 488 501 510 536 Likelihood function 400 427 Likelihood function for continuous sample space 435—37 Likelihood function, imprecise 431 Likelihood function, medial 431—32 Likelihood function, upper and lower 431 441 Likelihood inference (see Inference statistical likelihood) Likelihood principle 434—41 Likelihood principle for continuous sample spaces 435—40 Likelihood principle for discrete sample spaces 434—35 Likelihood principle for imprecise likelihoods 440—41 Likelihood principle, satisfied by natural extension 427 431—32 Likelihood principle, satisfied by regular extension 641 Likelihood principle, violated by frequentist inferences 583 Likelihood principle, violated by noninformative priors 229 232 583 Likelihood ratios, upper and lower 433 Lindley, D.V. 16 43 44 45 241 242 245 246 478 486 487 490 492 499 500 516 521 523 526 528 532 533 534 535 536 537 538 544 546 568 583 590 647 Lindman, H. 44 528 533 536 Linear programming 175 511 Linear space (see Space linear) Linear-vacuous mixture (see Mixture linear-vacuous) Linearity 66 86—89 609 linear Additivity) Linkage between prior and sampling model 399—400 405 423—24 Location (see Parameter location) Logic deductive 485 494 Logic deductive, fuzzy 50 265—66 538 Logic deductive, inductive (see also Interpretations of probability and prevision logical) Loomis, L.H. 493 Loss function (see Utility) Loss, axioms for 346 364 380 389 Loss, examples of 28 67 72 85 177 187 279 280 288 311 312 321—23 604 635—36 Loss, in non-statistical problems 28—29 67—72 114—16 Loss, in statistical problems 343—46 Loss, partial 344—45 Loss, sure 346 Luce, R.D. 660 Machlup, F. 524 Mackenzie, B.D. 481 Mallows, C.L. 488 565 590 Mamdani, A. 669 Mann, L. 484 Mansfield, U. 524 Manski, C.F. 491 513 517 518 536 Mapping, multivalued 182—84 273—74 March, J.G. 488 Marginalization 181—82 Marginals 181—82 314 Marginals, compatible 453 Marginals, independent 448 (see also Prevision joint) Market economics 65 72 493 627—28 Martin, A.W. 538 Maximality in preference ordering 161 Maximality in preference ordering, relation to Bayesian optimality 162 63 165—66 McClure, J. 47 517 Mean, invariant 140 Measurability Lebesgue 98 149—50 Measurability Lebesgue with respect to a field 129 306 Measurability Lebesgue with respect to a partition 291 306 Measure construction of integral from 128—29 (see also Additivity countable) Measurement biased, biases in 624—28 631 Measurement biased, bookmaking procedure 625—28 Measurement biased, comparison with standard events 196—97 Measurement biased, for comparing assessors 630 632—35 Measurement biased, general elicitation procedure 168—74 Measurement biased, imprecise 250 329 436—40 Measurement biased, model for 399—400 405 423—24 Measurement biased, multiple-price procedure 628—29 630 Measurement biased, scoring rules, see Scoring rules symmetric procedure 629—33 Measurement biased, two-sided betting procedure 243 624—25 Medical diagnosis 40 50 529 700 Mellor, D.H. 44 352 354 480 481 482 483 499 500 510 521 534 536 537 545 547 559 562 563 564 624 Membership function 261—66 Membership function, assessment of 262 264—65 Membership function, Zadehb’s rules of combination 265—66 Menges, G. 530 Methods of statistical inference (see Inference statistical) Mill, J.S. 43 526 Minimax decision (see Decision rules Action minimax) Minimax theorem 613 Mitchell, A.F.S. 528 Mixture (see Convex combination) Mixture, linear-vacuous 93—94 135 147 202—03 Mixture, preserved under conditioning 309 311—12 325 Model building, statistical 35—37 38 359—60 467—68 assessment) Models, approximate 355—56 Models, construction of 359—60 467—68 Models, continuous 435—40 Models, hierarchical 37 232 259—60 Models, imprecise 356—60 399—400 405 423—24 430—34 440—41 467—71 Models, interpretations of (see Interpretations of probability and prevision robust) Money pump 28 Monotonicity complete 272 Monotonicity complete of preferences 154 156 Monotonicity complete of previsions 76 88 2— 130 Mood, A.M. 569 Moore, G.H. 504 505 506 Moore, P.G. 510 Moreno, E. 517 518 536 Morgenstem, O. 490 492 Moses, L.E. 491 Mosteller, F. 487 500 536 544 565 Murphy, A.H. 536 MYCIN 50 Nachbin, L. 568 Nagel, E. 565 Namioka, I. 506 608 Nathanson, S. 484 Natural extension (see Extension natural) Nau, R.F. 489 536 538 Nazaret, W.A. 538 Near-ignorance (see Ignorance near Near-ignorance, constant odds-ratio (see Odds ratio constant) Neyman, J. 11 22 42 112 235 377 386 483 569 572 573 Ng, K. — F. 506 Nisbett, R.E. 483 488 Norman, R. 481 Novick, M.R. 228 521 525 590 686 Nuclear risk 246 Objectivity different, meanings of 111—14 Observation 284 336—37 Observation, continuous 328—32 436—40 Observation, modelled as an event 284 336—38 Observation, preserved under conditioning 309—10 Observation, preserved under statistical updating 401 Observation, unexpected 336 525 Observation, unreliable 274 276 339 Okuda, T. 538 Olshen, R.A. 571 Papamarcou, A. 49 564 592 Paradox of ideal evidence 220 PARAMETER 349 Parameter space 349 362 Parameter, learning 219 Parameter, location 229 372 383—84 Parameter, location-scale 232 373 Parameter, meaningful 350 465—66 Parameter, nuisance 357 468 Parameter, region of values 205 218 Parameter, scale 372 Parameter, true value 350 355—56 360 Pari-mutuel model (see Betting parimutuel Parikh, R. 507 559 Parnes, M. 507 559 Partition of possible observations 284 289 Pauker, S.G. 490 Pearl, J. 49 489 490 538 560 Pearman, A.D. 48 507 536 Pears, D.F. 484 Pearson, K. 521 Pedersen, J.G. 568 569 571 Peirce, C.S. 43 481 500 522 523 526 562 Penalty function (see Scoring rules) Pereira, C.A.B. 529 Pericchi, L.R. ix 479 497 500 510 517 518 525 528 529 535 536 537 538 559 568 576 584 Perks, W. 228 Permutability 457—60 Permutability and convergence of relative frequencies 465 Permutability as a structural judgement 473 475—76 Permutability, compared to exchangeability 460—62 Permutability, examples of 459 469 Permutability, grounds for 458 Permutation-invariance 111—13 (see Invariance Physicality) Phillips, L.D. 521 583 662 Pierce, D.A. 377 536 570 572 573 Pincus, D. 506 Pitz, G.F. 480 536 Polasek, W. 518 536 Popper, K.R. 480 500 501 522 562 563 564 565 Possibility 54—58 Possibility space 54 Possibility space in decision problems 24 239 Possibility space in statistical problems 362 Possibility space, arguments against 3—8 43—44 226—35 397 Possibility space, arguments for 235—53 Possibility space, axioms of 31—32 91—92 241—48 Possibility space, Bayesian dogma of 3 241 Possibility space, dogma of ideal 7 105—07 254—57 Possibility space, frequentist dogma of 564 Possibility space, ideal versus idealization 106—07 249 254 Possibility space, limits to 215 216 359 471 Possibility space, modifications of 56—57 180—86 337 38 Possibility space, not necessary for decision 236 243 Possibility space, observable 118 Possibility, apparent 55 Possibility, epistemic 55 Possibility, new 184—85 Possibility, practical 56 Possibility, pragmatic 56 185 Potter, J.M. 536 Prade, H. 50 538 539 669 Pratt, J.W. 515 516 533 545 547 572 601 Prediction, probabilistic 422 Prediction, versus explanation 360 466 preference 47 153—56 Preference, almost 153—54 Preference, axioms for, refer to Index of axioms 680 Preference, behavioural meaning 153 236—237 Preference, complete 157 241—47 Preference, correspondence with desirability 153 Preference, correspondence with linear previsions 158 Preference, correspondence with lower previsions 156 Preference, intransitive 28—29 Preference, more fundamental than prevision 159 Preference, real 616 Preference, role in decision making 160—62 Preference, strict 155—56 161 Preference, versus choice 236—37 242 247 Prevision 282—340 (see also Probability Interpretations Prevision, axioms for, refer to Index of axioms 680 Prevision, basic properties 76—80 Prevision, behavioural interpretation 61—63 Prevision, coherence with sampling model 362—67 Prevision, conglomerate 317 Prevision, constructed from conditional and marginal previsions 313—17 421—24 Prevision, constructed from independent marginals 452—57 Prevision, constructed from permutable marginals 459 475—76 Prevision, correspondence with other models 145 147 156 Prevision, defined through generalized Bayes rule 400—03 427 432 Prevision, determined by additive probability 91 128—29 Prevision, envelopes of, see Envelopes extensions of 136—39 Prevision, examples of 92—101 Prevision, exchangeable 460—61 Prevision, ideal 105—07 254—57 258—59 Prevision, independent (see also Prevision, product) 452 Prevision, invariant 139—45 Prevision, linear 66 86—92 Prevision, may be less precise than prior prevision 223—26 298—300 433 551 Prevision, needed to measure uncertainty in conclusions 22 110 252 388 Prevision, non-conglomerable 311 312 321 23 Prevision, not determined by conditional and marginal previsions 404—05 423—24 Prevision, not determined by lower probability 82—84 177 Prevision, not determined by prior assessments 337—38 395—96 399—400 433—34 437—40 Prevision, permutable 457 Prevision, posterior 362 424 Prevision, regular 640—41 Prevision, regular Bayesian 438—39 Prevision, standard Bayesian 393—96 428 Prevision, true (see Ideal) Prevision, updated, Conglomerability contingent 284—89 (see also Prevision conditional) Prevision, vacuous 298 308 366—67 391—92 428—29 438 conditional Price for gamble buying 61 625 629—30 Price for gamble buying, contingent 284 Price for gamble buying, fair (buying and selling) 66 86 241 44 Price for gamble buying, selling 65 625 629 Prevision linear Prevision lower) Price for gamble buying, updated 284 303 305 Principle of indifference 227 267 Principle of insufficient reason (see Principle of indifference) Principle of maximum entropy (PME) 266—72 Principles of rationality 27—32 33—35 Prior prevision (see Prevision prior) Prisoners problem 279 299—300 Probability, additive 89—91 (see also Additivity Prevision linear) Probability, as a betting rate 82 602—03 Probability, classificatory 188—91 197 248 Probability, comparative 45—46 191—97 241 244—46 600—01 Probability, comparison with other scientific concepts 249—50 Probability, conditional (see Prevision conditional Probability, correspondence with linear prevision 91 128—29 Probability, examples of 259 271 Probability, imprecise 260—61 Probability, unconditional (see Probability lower Probability, vacuous (see Prevision vacuous Probability, zero-one valued 100—01 147—50 Propositions 491 Psychology of action 17—20 Psychology, experimental studies of decision and indeterminacy 48 116—17 254 632—34 Purves, R.A. 579 Putnam, H. 488 Quantiles, upper and lower 204 quantum mechanics 358 480 491 Quinlan, J.R. 50 513 Radioactivity 352 Radon — Nikodym derivative 436 574 Raiffa, H. 241 516 518 519 521 523 531 532 533 545 547 Ramsey, F.P. 43 45 241 243 244 249 481 483 488 489 490 491 494 531 534 545 548 562 Random quantity 57—58 (see also Gamble Random variable) Random quantity, Aristotelean 484 Random quantity, bounded 40—41 599 Random quantity, external 27—28 33—42 113 Random quantity, internal 27—32 42 Random quantity, principles of (see Principles of rationality versus reasoning) Randomization in decision making 162 Randomization in experimental design 299 Randomness 358 (see also Chance) Randomness, versus ignorance 113—14 212 Rapoport, A. 672 Rasmuson, D.M. 532 Rawls, J. 484 485 Raz, J. 481 Reason, limitations of 40—41 116—17 241
Ðåêëàìà
|
|
Î ïðîåêòå