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Bayesian Nets and CausalityPhilosophical and Computational Foundations$

Jon Williamson

Print publication date: 2004

Print ISBN-13: 9780198530794

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198530794.001.0001

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(p.235) INDEX

(p.235) INDEX

Source:
Bayesian Nets and Causality
Publisher:
Oxford University Press
κ-ancestral, 99, 100
ρ-ancestral, 177
, 4
@, 4
, 15
Abductive logic programming, 195
Abductive reasoning, 195, 201
Acyclic, 166
Adding‐arrows, 24
Additional language, 209
Additivity, 5
Agent‐relative, 7
Aleatory, 7
Almost everywhere, 143
Ancestors, 14
Ancestral, 99, 177
Ancestral order, 18
Anti‐physical, 131
Approximate inference algorithm, 20
Approximation subspace, 21
Argumentation framework, 172
Arntzenius, 55
Arrow weight, 22
Arrows, 14
Artificial intelligence, 195
Assignment, 4
Atomic state, 175
Axiom, 176
Axiom of Convergence, 8
Axiom of Independence, 9
Axiom of Randomness, 8
Bacon, 120, 121
Balanced adding‐arrows algorithm, 38
Bayes' theorem, 12, 149
Bayesian, 11
Bayesian conditionalisation, 12, 71, 194, 209, 210
Bayesian multinets, 169
Bayesian network, 14
Belief function, 11
Bench‐Capon, 173
Bernoulli, 66–70, 77
Betting quotient, 11, 203
Blocks, 16
Bridge language, 202, 209
Calibration Principle, 70–77, 79, 80, 83, 106, 143
Carnap, 189, 190, 207
Cartwright, 56
Causal connection, 131
Causal consistency, 157
Causal Dependence, 61, 62, 108, 112, 113, 115–117, 137, 139, 142, 160, 181, 182
Causal dispositions, 134
Causal graph, 122, 130
Causal influence, 178
Causal Irrelevance, 99–101, 105–107, 150, 168, 177, 217
Causal Markov Condition, 1, 50–54, 57–64, 105, 107, 112, 113, 115, 122–129, 136, 137, 140–144, 148–151, 157, 159, 160, 165, 166, 168, 172, 181
Causal net, 49, 122
Causal Sufficiency, 124, 125
Causal supergraph, 158
Causal supernet, 161
Causal to Probabilistic Transfer, 101, 150, 175, 186
Causally consistent, 158, 159
Causally interpreted Bayesian network, 49
Cccc, 159
Chain, 16, 158
Chain rule, 17
Chance, 10
Chance fixers, 76
Children, 14
Christensen, 206
Coherent, 11
Coherence, 206
Collective, 8
Compatible, 99, 216
Complete, 99, 179
Complete graph, 19
Components (of a Bayesian network), 14
Computational linguistics, 195
Concept learning, 195
Conditional mutual information, 22
Conditional probability function, 5
Confirmation theory, 195
Confluence, 179
Conjunction, 175
Conservative, 210
Conservativity principle, 197, 202
Consistent, 4, 163
Constraint graph, 86
(p.236) Constraint independence, 88, 142, 145
Constraint‐set independence, 88, 91, 92
Construction problem, 19
Continuity, 82
Contraction, 16, 141, 142, 166
Convenience, 135
Cooper, 125
Counterfactual, 116
Covering‐law, 119
Cross entropy, 22, 24, 95, 210
Cross entropy updating, 71, 211
Cumulative distribution function, 6
D‐separates, 16, 17, 137, 160
De Finetti, 12, 75, 76, 106
Decomposition, 16, 17
Definite clauses, 183
Definite logic program, 183
Depends causally, 115
Depth, 156
Descendants, 14
Direct inferior, 156
Direct superior, 156
Directed acyclic graph, 14
Directed constraint graph, 90, 142
Directed path, 16
Directed‐path singly connected, 20
Discrete network, 31
Disfluence, 179
Disjunction, 175
Distribution, 6
Distribution function, 6
Divine intervention, 139
Doctrines, 135
Dowe, 111, 114
Dutch book, 11
Earman, 195, 207, 208
Effluence, 179
Empirical, 66
Empirically based subjective probability, 66
Entropy, 23
Epistemic causality, 130
Epistemic impartiality, 206
Epistemic probability, 65
Epistemological, 7
Equivalence, 82, 175
Equivalencies, 16
Essential graph, 144
Exchangeable, 12, 75, 147
Exclusion, 121
Explanation, 135
Factorise, 87, 91
Faithful, 144
Faithfulness, 62, 124, 144
Family notation, 14
Fast Causal Inference, 124
FCI algorithm, 124
Fermat's Last Theorem, 179
Finite, 156
First harvest, 121
Flattening, 165–168, 172
Foundational, 206
Frequency, 7
Frey, 178
Fronhöfer, 94
Gaifman, 13
Gambling system, 8
Gardenfors, 207
Garside, 94
Global Markov Condition, 87, 102, 213
Glymour, 123, 124
Goodman, 197, 198
Greedy search, 38
Grue, 197–198
Harman, 206, 217
Heckerman, 125
Hempel, 119, 189
Herskovitz, 125
Hierarchical Bayesian nets, 171
Holmes, 94
Hope, 74
Howson, 190, 191, 194, 195, 196, 198, 199
Hughes, 74
Hume, 131–133
Hunter, 95–97
Hypothesise, 148, 149
Hypothetico‐deductive, 118, 119
IC algorithm, 124, 125
Implication, 175
Incomplete, 179
Indefinite propositions, 188
Independence, 82
Induction, 120, 121
Inductive, 118
Inductive Causation, 124
Inductive Logic Programming, 184, 195
Inference problem, 20
Inferior, 156
Influence relation, 177
Interior, 158
Interprets, 176, 191
Intersection, 16, 143
Intervention, 139
Irrelevance, 178
Irrelevant, 99, 100
Irrelevant Information, 82
(p.237) James, 203
Jaynes, 2, 79–81, 108, 190, 195, 207
Jeffrey conditionalisation, 211
Jeffreys, 189, 190
Joint distribution, 6
Kant, 131–134
Keynes, 68, 70, 78, 79, 189, 190
Knowledge revision strategy, 209
Korb, 74
Kuhn, 201, 202, 208
Lakatos, 194, 200, 207
Language, 175
Language change update strategy, 209
Language invariance, 196
Laplace, 67, 68, 70, 72, 79, 80
Law of causality, 133
Lehrer, 205, 206
Level 0, 156
Level 1, 156
Level 2, 156
Lewis, 13, 73, 115, 116, 119
Literal, 175
Logic programming, 183
Logical, 66
Logical Bayesian net, 179
Logical Dependence, 182, 183
Logical graph, 179
Logical implication, 176
Logical influence, 178, 179
Logical interpretation of probability, 188
Logical Markov Condition, 179
Logical net, 179
Logical to Probabilistic Transfer, 185, 186
Logically based subjective probability, 66
Logically omniscient, 187
Lukasiewicz, 188, 190
Lycan, 204
Marginal probability function, 5
Markham, 94
Markov Chain Monte Carlo, 127
Markov Condition, 15–18, 50, 144, 166, 167, 179, 182
Markov consistent, 159, 160
Markov equivalent, 144
Markov net, 89, 185
Maxent, 80, 95, 96
Maxent update strategy, 217, 218
Maximally forgetful, 209
Maximally retentive, 209
Maximin update strategy, 209, 210
Maximum cardinality search, 90
Maximum Entropy Principle, 1, 79–85, 95, 106, 150, 168, 210
Meek, 125
Mendeleev, 201
Mental, 7, 130
Mental / Physical, 7
Mental causality, 51
Mental‐Physical Calibration Principle, 71, 73
Menzies, 116, 117
Mill, 51
Mind projection fallacy, 2, 108, 190
Minimality, 16, 124
Minimum cross entropy updating, 94
Minimum Description Length, 38, 126
Minimum Message Length, 126
Missing values, 33
Mixed cause, 113
Models, 176, 191
Modus ponens, 176
Moral graph, 91, 212
Multipliers, 86, 212
Natural kinds, 197
Negation, 175
Negative cause, 113
Negative logical influence, 178
Network arguments, 173
Network variable, 155
Network weight, 22
Non‐recursive, 156
Object‐oriented Bayesian nets, 170
Objective, 7, 130
Objective Bayesian semantics, 191
Objective Bayesianism, 11, 65
Objects, 170
Obstinacy, 82
Oppenheim, 119
Pólya, 120
Parents, 14
Paris, 182, 83 193
Partial entailment, 187
Path, 16
PC algorithm, 123–125
Pearl, 83, 95, 124, 135–137
Pearl's puzzle, 95
Peers, 156
Percentage success, 31
Perfect, 90
Perfectly calibrated, 74
Personalist, 7
Philosophy of science, 195
Physical, 7, 130
Physical causality, 51
(p.238) Place selection, 8
Popper, 9, 10, 11, 13, 118–121, 129, 148
Positive cause, 113
Positive logical influence, 178
Predict, 74, 148, 149, 151
Predictive accuracy, 74
Predictive inference, 20
Presentation, 120
Preventative, 113
Price, 116, 117
Principle of Indifference, 68–70, 79, 80, 83, 199
Principle of the Common Cause, 51–55, 112, 113, 115, 128
Probabilistic consistency, 158
Probabilistic entailment, 191–193
Probabilistic semantics, 188
Probabilistic to Causal Transfer, 140, 142, 147, 150, 175, 186
Probabilistic to Logical Transfer, 185, 186
Probabilistically consistent, 161
Probability distribution, 6
Probability function, 5
Probability specification, 14
Probability table, 14
Probability tree, 128
Projectible, 197
Prolog, 183, 184
Proof, 176
Propensity, 9
Propositional entailment, 188
Propositional variable, 175
Proves, 176
Qualified Causal Dependence, 137–139
Quine, 205
Railton, 119
Ramsey, 131, 133, 134, 189, 190
Recovery, 42, 43
Recursive, 8
Recursive argumentation network, 173
Recursive Bayesian multinets, 169
Recursive Bayesian net, 152, 156
Recursive causal graph, 153
Recursive causal net, 156
Recursive causality, 153
Recursive logical net, 180, 181
Recursive Markov Condition, 165, 166, 168, 171
Recursive relational Bayesian nets, 169
Recursive structural equation model, 172
Reference class problem, 10, 13, 76
Reichenbach, 7, 51, 112
Relational Bayesian nets, 170
Relativisation, 82
Relevance set, 100
Renaming, 82
Repeatable, 7, 115
Repeatably instantiatable, 7
Rhodes, 94
Ribet, 178
Rosen, 113
Rule of inference, 176
Running intersection property, 90
Russell, 119, 133
Salmon, 56, 111, 113, 114
Sampling bias, 33
Scheines, 123, 124
Schramm, 94
Scoring function, 125
Screen off, 51
SEM‐variables, 172
Semantically influences, 179
Sentences, 175
Separates, 86, 87
Shafer, 127, 128
Shannon, 82
Sharpening challenge, 78
Simple arguments, 173
Simple variable, 155
Simplicity, 199
Simplification, 157
Single‐Case / Repeatable, 7
Singly connected, 20
Situation, 128
Size, 19
Skeleton, 144
SLP, 184
Snir, 13
Sober, 52, 53
Space complexity, 44
Spirtes, 123, 124
Stable, 144
Stage One, 109
Stage Two, 109
Standard probabilistic semantics, 191
State, 175
State description, 175
Statistical learning theory, 195
Stochastic Logic Programming, 184
Strategic Causal Dependence, 139, 142, 148, 150
Strategic dependence, 139, 140, 142
Strategically compatible, 142–144
Strategically consistent, 140–143
Strategy, 137–139
Strict personalism, 65
Strict subjectivism, 65
Structural equation model, 104, 122, 171–172
(p.239) Subchain, 158
Subjective, 7, 130
Subjective /Objective, 7
Subjective Bayesianism, 11, 65
Superior, 156
Suppes, 112
Symmetry, 16
Taniyama‐Shimura Conjecture, 179
Target, 18
Test, 148, 149, 151
Time complexity, 44
Token‐level, 7
Transfer, 101, 140, 178
Transitional knowledge, 209
Triangulated, 89
Tuth Principle, 70
Type‐level, 7
U‐random, 32
Ultimate belief, 13
Ultimate causal relations, 147
Underdetermination, 198
Undirected constraint graph, 142
Undogmatic, 13
Unobserved variable, 33
Update, 148, 149
Update strategy, 209
Urbach, 198
V‐structure,144
Valuation, 175
Value, 4
Variable, 4
Vencovská, 82, 83
Venn, 7
Verma, 124
Von Mises, 7–9
Washed out, 195
Weak Union, 16, 141, 142
Well‐founded, 156