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Conditional Independence
, 1997
"... This article has been prepared as an entry for the Wiley Encyclopedia of Statistical Sciences (Update). It gives a brief overview of fundamental properties and applications of conditional independence. ESS Update A. P. Dawid Conditional Independence Ancillarity; axioms; graphical models; markov pro ..."
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This article has been prepared as an entry for the Wiley Encyclopedia of Statistical Sciences (Update). It gives a brief overview of fundamental properties and applications of conditional independence. ESS Update A. P. Dawid Conditional Independence Ancillarity; axioms; graphical models; markov properties; sufficiency. The concepts of independence and conditional independence (CI) between random variables originate in Probability Theory, where they are introduced as properties of an underlying probability measure P on the sample space (see CONDITIONAL PROBABILITY AND EXPECTATION). Much of traditional Probability Theory and Statistics involves analysis of distributions having such properties: for example, limit theorems for independent and identically distributed variables, or the theory of MARKOV PROCESSES. More recently, it has become apparent that it is fruitful to treat conditional independence (and its special case independence) as a primitive concept, with an intuitive meaning, ...
Structurebased causes and explanations in the independent choice logic
 Proceedings UAI2003
, 2003
"... This paper is directed towards combining Pearl’s structuralmodel approach to causal reasoning with highlevel formalisms for reasoning about actions. More precisely, we present a combination of Pearl’s structuralmodel approach with Poole’s independent choice logic. We show how probabilistic theor ..."
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Cited by 13 (6 self)
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This paper is directed towards combining Pearl’s structuralmodel approach to causal reasoning with highlevel formalisms for reasoning about actions. More precisely, we present a combination of Pearl’s structuralmodel approach with Poole’s independent choice logic. We show how probabilistic theories in the independent choice logic can be mapped to probabilistic causal models. This mapping provides the independent choice logic with appealing concepts of causality and explanation from the structuralmodel approach. We illustrate this along Halpern and Pearl’s sophisticated notions of actual cause, explanation, and partial explanation. Furthermore, this mapping also adds firstorder modeling capabilities and explicit actions to the structuralmodel approach.
Knowing and reasoning in
 in College: Gender Related Patterns in Student’s Intellectual Development
, 1992
"... Modelling a decision support system for ..."
Contextual Weak Independence in Bayesian Networks
 Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, 670679
, 1999
"... It is wellknown that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called contextstrong independence (CSI), can be used to facilitate the acquisition, representation ..."
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Cited by 11 (5 self)
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It is wellknown that the notion of (strong) conditional independence (CI) is too restrictive to capture independencies that only hold in certain contexts. This kind of contextual independency, called contextstrong independence (CSI), can be used to facilitate the acquisition, representation, and inference of probabilistic knowledge. In this paper, we suggest the use of contextual weak independence (CWI) in Bayesian networks. It should be emphasized that the notion of CWI is a more general form of contextual independence than CSI. Furthermore, if the contextual strong independence holds for all contexts, then the notion of CSI becomes strong CI. On the other hand, if the weak contextual independence holds for all contexts, then the notion of CWI becomes weak independence (WI) which is a more general noncontextual independency than strong CI. More importantly, complete axiomatizations are studied for both the class of WI and the class of CI and WI together. Finally, the interesting property of WI being a necessary and sufficient condition for ensuring consistency in granular probabilistic networks is shown. 1
The New Challenge: From a Century of Statistics to an Age of Causation
 COMPUTING SCIENCE AND STATISTICS
, 1997
"... Some of the main users of statistical methods  economists, social scientists, and epidemiologists  are discovering that their fields rest not on statistical but on causal foundations. The blurring of these foundations over the years follows from the lack of mathematical notation capable of disti ..."
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Some of the main users of statistical methods  economists, social scientists, and epidemiologists  are discovering that their fields rest not on statistical but on causal foundations. The blurring of these foundations over the years follows from the lack of mathematical notation capable of distinguishing causal from equational relationships. By providing formal and natural explication of such relations, graphical methods have the potential to revolutionize how statistics is used in knowledgerich applications. Statisticians, in response, are beginning to realize that causality is not a metaphysical deadend but a meaningful concept with clear mathematical underpinning. The paper surveys these developments and outlines future challenges.
Probabilities of causation: Three counterfactual interpretations and their identification
 SYNTHESE
, 1999
"... According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, ..."
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Cited by 11 (5 self)
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According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, for the probability that event x was a necessary or sufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient) causation can be learned from statistical data, and shows how data from both experimental and nonexperimental studies can be combined to yield information that neither study alone can provide. Finally,weshow that necessity and sufficiency are two independent aspects of causation, and that both should be invoked in the construction of causal explanations for specific scenarios.
Causes and Explanations in the StructuralModel Approach: Tractable Cases
 IN PROC. EIGHTEENTH CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE (UAI 2002
, 2002
"... In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structuralmodel approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which show that under suitable restrictions deciding ..."
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Cited by 10 (3 self)
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In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structuralmodel approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which show that under suitable restrictions deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability results for the structuralmodel approach.
Complexity Results for Explanations in the StructuralModel Approach
 Institut für Informationssysteme
, 2002
"... We analyze the computational complexity of Halpern and Pearl's (causal) explanations in the structuralmodel approach, which are based on their notions of weak and actual causality. In particular, we give a precise picture of the complexity of deciding explanations, partial explanations, and ..."
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Cited by 6 (5 self)
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We analyze the computational complexity of Halpern and Pearl's (causal) explanations in the structuralmodel approach, which are based on their notions of weak and actual causality. In particular, we give a precise picture of the complexity of deciding explanations, partial explanations, and partial explanations, and of computing the explanatory power of partial explanations.
Probabilities of causation: Bounds and identi cation
 In Proceedings of the Sixteenth Conference on Uncertainty in Arti cial Intelligence
, 2000
"... This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show howto optimally bound these quantities from data obtained in ex ..."
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Cited by 6 (5 self)
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This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structuralsemantical de nitions of the probabilities of necessary or su cient causation (or both), we show howto optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the datagenerating process. In particular, we strengthen the results of Pearl (1999) by weakening the datageneration assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attributionrelated problems of decision making. 1
Caveats for Causal Reasoning with Equilibrium Models
, 2003
"... Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recur ..."
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Abstract. In this paper 1 we examine the ability to perform causal reasoning with recursive equilibrium models. We identify a critical postulate, which we term the Manipulation Postulate, that is required in order to perform causal inference, and we prove that there exists a general class F of recursive equilibrium models that violate the Manipulation Postulate. We relate this class to the existing phenomenon of reversibility and show that all models in F display reversible behavior, thereby providing an explanation for reversibility and suggesting that it is a special case of a more general and perhaps widespread problem. We also show that all models in F possess a set of variables V ′ whose manipulation will cause an instability such that no equilibrium model will exist for the system. We define the Structural Stability Principle which provides a graphical criterion for stability in causal models. Our theorems suggest that drastically incorrect inferences may be obtained when applying the Manipulation Postulate to equilibrium models, a result which has implications for current work on causal modeling, especially causal discovery from data. 1