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Shafer G. — The Art of Causal Conjecture
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Название: The Art of Causal ConjectureАвтор: Shafer G. Аннотация: In The Art of Causal Conjecture, Glenn Shafer lays out a new mathematical and philosophical foundation for probability and uses it to explain concepts of causality used in statistics, artificial intelligence, and philosophy. The various disciplines that use causal reasoning differ in the relative weight they put on security and precision of knowledge as opposed to timeliness of action. The natural and social sciences seek high levels of certainty in the identification of causes and high levels of precision in the measurement of their effects. The practical sciences — medicine, business, engineering, and artificial intelligence — must act on causal conjectures based on more limited knowledge. Shafer's understanding of causality contributes to both of these uses of causal reasoning. His language for causal explanation can guide statistical investigation in the natural and social sciences, and it can also be used to formulate assumptions of causal uniformity needed for decision making in the practical sciences. Causal ideas permeate the use of probability and statistics in all branches of industry, commerce, government, and science. The Art of Causal Conjecture shows that causal ideas can be equally important in theory. It does not challenge the maxim that causation cannot be proven from statistics alone, but by bringing causal ideas into the foundations of probability, it allows causal conjectures to be more clearly quantified, debated, and confronted by statistical evidence.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 511Добавлена в каталог: 22.10.2010Операции: Положить на полку |
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accounting for 429 Adams, W.J. 406 Affect see "To affect" Algebra 396 Analysis of variance see "Partition of variance and covariance" Ancestor 233 386 Andersen, Per Kragh 253 Arntzenius, Frank 153 Assemblage 477 Asymmetry 393 Attribution 316 Axiom(s) for Doob catalogs 262 Axiom(s) for event trees 233 Axiom(s) for independence 186—188 450—452 Axiom(s) for lifting 284—285 Axiom(s) for martingales 79 257 Axiom(s) for probability catalogs 81 Axiom(s) for probability in event trees 68 Axiom(s) for probability measures 399 Axiom(s) for refining 283 Axiom(s) for regular event trees 240—241 Axiom(s) for simplifying 285 Axiom(s) of additivity 399 Axiom(s), intersection 452 Bar-Hillel, M. 111 Baron, Reuben M. 317 Barwise, Jon 375 Bayes net 366—368 Bayes, Thomas, event tree reasoning 61 62 Bayes, Thomas, independence 133 Bayes, Thomas, subsequent events 42 Bayesian reasoning as analogy 110 Bayesian reasoning, use of sample-space framework 91—92 Belnap, Nuel, intersecting event tree 60 Belnap, Nuel, next situation 241 Bennett, Jonathan 43 Bentler, Peter 462 Bernardo, Jose M. 110 Bernert, Christopher 357 Bernoulli, Jacob, gambler's ruin 380 Bernoulli, Jacob, law of large numbers 406 Bernoulli, Jacob, maxims 300 Bernoulli, Jacob, subjectivity 1 105 Binary relation 393 Birkhoff, Garrett 393 Blalock, H.M. 456 Bollen, Kenneth A. 454 464 Borchardt, Gary C. 378 Boudon, Raymond 456 Branching probabilities 5 69 265 Breslow, N.E. 330 Bryant, Randal 363 Buntine, Wray L. 360 Canonical event tree 55 Cartwright, Nancy 133 Catalog 261 see Catalog, completion of 267 Catalog, Doob 262 Catalog, fair-bet 262 Causal conjecture, distinguished from proof 15 Causal conjecture, maxims for 301 Causal diagrams, independence 341 Causal diagrams, joint 20—23 339—342 Causal diagrams, linear-sign 339 Causal diagrams, mean tracking 339 Causal diagrams, singular 147—149 Causal diagrams, strong tracking 339 Causal diagrams, uncorrelatedness 341 Causal diagrams, unpredictability 341 Causal explanation, diversity of 302 Causal explanation, purpose of 304 Causal interpretation of conditional independence 16 Causal interpretation of partial uncorrelatedness 16 Causal interpretation of regression coefficient 16 313 314 Causal interpretation of statistical prediction 334—335 Causal law as rule governing intervention 27 Causal law as rule of construction 108 Causal law in type theory 377—378 Causal models 331—357 Causal relations among Moivrean events 10 Causal relations among Moivrean variables 11—12 Cause see also "Common causes" "Effect" Cause, average effect of 17—19 305—311 Cause, dynamic nature of 14 Cause, misuse of the word 13 18—19 160—162 304 336 Chain 385 Chance situation 249 265 Change in belief 101—106 Charniak, Eugene 369 Chebyshev's inequality 405 Child 386 Coarsening 397 Collider 388 457 Colon, use in definitions 41 Common causes, basis of causal relations 12—13 Common causes, dimensionality of 353—355 Common causes, partial and complete 149—151 Common causes, source of correlation 121—128 Comparative evidence 15—16 322 343 Complement 43 Concomitant 314 Concomitant, cut 54 246 313 Concomitant, Moivrean event as 18 Concomitant, Moivrean variable as 54 Conditional distribution for prediction 333 Conditional distribution in sample space 411 Conditional expectation 64 87 410 412 Conditional expected value as tracking function 205 Conditional expected value in probability tree 64 87 Conditional expected value in sample space 407 Conditional independence and tracking 142—143 190—192 Conditional independence for Moivrean events 128—133 Conditional independence for Moivrean variables 175—177 Conditional independence in sample space 431 Conditional probability as revised belief 102 Conditional probability as tracking probability 142 194 Conditional probability in probability tree 64 73 Conditional probability in sample space 406 Conditional probability, novelty of 104 Configuration in assemblage 477 Configuration in event tree 52 Configuration in sample space 401 Conjunctive fork 150 Constable, Robert L. 371 374 Construction of probability tree 108 360 Construction ordering 341 387 Construction ordering, not needed for independence and uncorrelatedness diagrams 341 Construction ordering, not needed for Markov and linear relevance diagram 468 Cornfield, Jerome 336 Correlation coefficient 14 438 Correlation coefficient and regression coefficient 438 Correlation coefficient in a situation 79 Cost 270 Counterfactual 108 Covariance 77 403 Covariance structure model 462 Covariance structure model, recursive 464 Covariate 315 Cox, D.R. 253 329 330 Cross-sectional evidence 322 see Cut 39 235 Cut of situation 41 235 Cut, daughter 41 Cut, expectation in 83 Cut, identification of 51 53 Cut, initial 40 Cut, lattice of cuts 40 238—239 Cut, ordered with situation 237 Cut, partial 41 235 Cut, proper 40 Cut, resolving 41 245 Cut, terminal 40 d-connection 388 D-Separation 341 388 daughter 34 233 386 Davey, B.A. 393 Dawid's axioms 186—188 341 450—452 469 Dawid, A.P., axioms 187 450 452 Dawid, A.P., Jeffreys's law 406 Dawid, A.P., long-run aspects of probability 111 Dawid, A.P., sequential prediction 107—108 Day, N.E. 330 De Moivre, Abraham, concept of event 23 De Moivre, Abraham, event-tree reasoning 61 De Moivre, Abraham, gambler's ruin 380 De Moivre, Abraham, varying probability tree 104 De Mori, Renato 369 Decision 360 Decision situation 249 265 Decision tree 62 249—253 Dedekind cut 235 Dempster, A.P. 330 369 Dependence diagram 366 480 Descartes, Rene 380 Descendant 233 386 Determinacy for family of Moivrean variables 53 Determinacy for Moivrean events 37 Determinacy for Moivrean variables 50 244 Determinacy for partitions 52 Determinism 72 234 Direct effect 458 Direct effect, causal interpretation 345 Directed acyclic graph 386 Directed acyclic graph, collider 388 457 Directed acyclic graph, construction ordering for 341 387 Directed acyclic graph, moral graph for 388 Directed acyclic graph, ordered 341 387 Directed chain 386 Directed cycle 386 Directed graph 386—391 Directed path 386 Directed tree 386 Divergence of Humean events 47 246 Divergence of situations 233 Doob closure 262 Doob, J.L. 262 399 Draper, David 17 Druzdzel, Marek 378 472 Duffle, Darrell 62 Edwards, A.W.F. 6 31 62 365 380 Eerola, Mervi 6 Effect in path analysis 345 458 Effect of Humean variable 311—315 Effect of Moivrean event 305—311 Embedding 55 480—482 Empirical relevance 107 Empirical success 106 Endogenous node 386 Endogenous variable 331 Engel, Arthur 365 Engel, Eduardo M.R.A. 32 Engle, R.F. 345 Estimation 13 127—128 360 Ethics of causal talk 160—162 304 Evaluate see "To evaluate" Event see "Humean event" "Moivrean Event tree 31—62 Event tree as partially ordered set 232—240 Event tree as set of sets 230—232 Event tree for stochastic process 54 Event tree with absolute time scale 57 Event tree with relative time scale 57 Event tree, abstract 229—246 Event tree, intersecting 60 Event tree, regular 240—244 evidence 13—17 109 Evidence, comparative 15—16 322 343 Evidence, longitudinal 13 322 343 Exogenous node 386 Exogenous variable 331 Expectation 412 Expectation as a martingale 267 Expectation expression 413 Expectation in a cut 80 83 Expectation in a situation 64 87 267 Expectation of martingale 80 Expectation, conditional 64 87 410 412 Expectation, interpretation of 95—98 Expectation, lower and upper 269 Expected value 402—405 Expected value in a situation 64 74 267 Expected value, conditional 64 87 410 Expected value, interpretation 92—95 Expected value, lower and upper 269 Experiment as cause 12 121 Experiment in nature's tree 6 Experiment, randomized 109 320—322 Factor 315 Factor analysis 460 failing 37 Fair bet 256 261 Fair-bet catalog 262 Falk, R. 111 Family of Moivrean variables 52—53 Family of Moivrean variables in statistical prediction 337 Family of Moivrean variables, causal relevance 338 Family of Moivrean variables, empty 52 Family of Moivrean variables, identifies cut 53 Family of variables in a sample space 401—402 Family of variables in a sample space, independent 443 Family of variables in a sample space, intersection 401 Family of variables in a sample space, linearly identifies itself 402 Family of variables in a sample space, subfamily 401 Family of variables in a sample space, union 401 Farkas's lemma 264 Fermat, Pierre 379—380 Fetzer, James H. 133 Filter 42 96 Filtration 59 398 Filtration, scaled 60 398 Fisher, Ronald A. 321 330 Forecasting 360 Forecasting system 107 Formal coefficient 223 Formal independence for Moivrean events 115 118 Formal independence for Moivrean variables 171 174 Formal independence, given a Moivrean event 129 Formal independence, posterior to a Moivrean event 129 Formal independence, posterior to a situation 128 Formal score function 226 Formal sign 154 219 Formal sign for families of variables 228 Formal sign, linear 223 Formal sign, scored 226 Formal sign, weak 159 Formal uncorrelatedness 173 Formal uncorrelatedness for more than two Moivrean variables 174 Formal unpredictability in mean 172 Frame for abstract variable 477 Frame for family of variables 52 401 Frame for variable 49 400 Freedman, David A., causal models in social science 357 Freedman, David A., path diagrams 453 460 Freedman, David A., unstandardized coefficients 344 462 frequency 100—101 Freund, John E. 102 Fully informed 296 Functional dependence 203 Functional dependence, weakness as condition 338—340 Gain 96
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