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Causal inference in statistics: An Overview
, 2009
"... This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all ca ..."
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Cited by 68 (11 self)
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This review presents empirical researcherswith recent advances in causal inference, and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potentialoutcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.
Probabilities of Causation: Bounds and Identification
 Annals of Mathematics and Artificial Intelligence
, 2000
"... This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical definitions of the probabilities of necessary or sufficient causation (or both), we show h ..."
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Cited by 22 (10 self)
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This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structuralsemantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the datagenerating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excessriskratio could be used for assessing attributional quantities such as the probability of causation. 1
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 ..."
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Cited by 18 (3 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.
On the Definition of Actual Cause
, 1998
"... This report is based on lecture notes written for CS 262C, Spring 1998, and is organized as follows. Following a review of the SL framework (Section 2) Section 3 provides a comparison to other approaches to causation and suggests an explanation of why the notion of actual cause has encountered diffi ..."
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Cited by 5 (1 self)
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This report is based on lecture notes written for CS 262C, Spring 1998, and is organized as follows. Following a review of the SL framework (Section 2) Section 3 provides a comparison to other approaches to causation and suggests an explanation of why the notion of actual cause has encountered difficulties in those approaches. Section 3 defines "actual cause" and illustrates, through examples, how the "probability that event X = x actually caused event
Causality in the Social and Behavioral Sciences
 A PAPER SUBMITTED TO SOCIOLOGICAL METHODOLOGY.
, 2009
"... This paper aims to acquaint researchers in the quantitative social and behavior sciences with recent advances in causal inference which provide a systematic methodology for defining, estimating, testing, and defending causal claims in experimental and observational studies. These advances are illust ..."
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Cited by 2 (1 self)
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This paper aims to acquaint researchers in the quantitative social and behavior sciences with recent advances in causal inference which provide a systematic methodology for defining, estimating, testing, and defending causal claims in experimental and observational studies. These advances are illustrated using a general theory of causation based on nonparametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 195060s, which provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and potentialoutcome frameworks, and develops symbiotic tools that use the strong features of both.
A Note on Causes of Effects Judea Pearl
, 2014
"... Interest in applying counterfactual logic to legal settings has resulted in disagreements regarding the proper interpretation of the legal term “but for, ” as in “It is more probable than not that the injury would not have occurred but for the defendant action ” (Robertson, 1997). Let A = 1 stands ..."
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Interest in applying counterfactual logic to legal settings has resulted in disagreements regarding the proper interpretation of the legal term “but for, ” as in “It is more probable than not that the injury would not have occurred but for the defendant action ” (Robertson, 1997). Let A = 1 stands for the defendant’s action, R = 1 for the observed response (e.g., injury or damage), and R0 (respectively R1) for the value that R would have had the action not taken (A = 0). The standard interpretation of the “but for ” criterion is captured by the inequality PN ≥ 0 where PN stands for counterfactual probably PN = P (R0 = 0A = 1, R = 1) (1) termed “probability of necessity ” in Pearl (2000a). The same interpretation was used by Greenland and Robins (1988); Balke and Pearl (1994a,b); Pearl (1999); Tian and Pearl (2000). Equation (1) is a direct translation of the “but for ” test into counterfactual language, saying that R would not have occurred in the absence of A, given that R and A did in fact occur. Implicit in PN is the understanding that the probability P is defined relative to a reference class of individuals who are exchangeable with the defendant. In other words, P embeds all other information we have about the incident, for example, that the defendant is a red hair lawyers who owns a black Mercedes, and that the claimant was a reckless driver. Ironically, Eq. (1) was also used in Pearl (2000b)to demonstrate that counterfactuals can handle CoEtype questions, while Dawid dismissed counterfactuals as “metaphysical” concepts that “can lead to distorted understandings and undesirable practical consequences” (Dawid, 2000, p. 408). “I challenge Dawid to express Query II [“My headache has gone. Is it because I took aspirin?”], let alone formulate conditions for its estimation in a counterfactualfree language (Pearl, 2000b, p. 429).
Article Causes of Effects and Effects of Causes
"... This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain c ..."
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This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation. We further investigate the circumstances under which such bounds can emerge, and the philosophical dilemma associated with determining individual cases from statistical data. Keywords probability of necessity, probability of causation, counterfactuals, legal liability, attribution
7. Author(s) 8. Performing Organization Report No.
, 2002
"... This report presents an approach to assess the effect of vehicle traffic volumes and speeds on pedestrian safety. It shows that the probability of standardized pedestrian conflict resulting in a collision can be computed given data on the distribution of vehicle speeds and headways on a residential ..."
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This report presents an approach to assess the effect of vehicle traffic volumes and speeds on pedestrian safety. It shows that the probability of standardized pedestrian conflict resulting in a collision can be computed given data on the distribution of vehicle speeds and headways on a residential street. Researchers applied this method to data collected on a sample of 25 residential streets in the Twin Cities and found that collision rates varied between four and 64 collisions per 1,000 pedestrian conflicts, depending primarily on the streets traffic volume. Using a model that relates the impact speed of a vehicle to the severity of pedestrian injury, they computed the probabilities of a severe collision. Sensitive to both traffic volume and traffic speed, the severe collision rate varied between one and 25 collisions between 1,000 conflicts. Using the same data, researchers also computed the crash reduction factor, used to assess the potential safety effect of a 25 miles per hour speed limit on the sample of residential streets. The estimated crash reductions ranged between.2 and 45 percent, depending primarily on the degree to which the vehicle speeds currently exceeded 25 miles per hour. Researchers also showed how this computation assists with the reconstruction of actual vehicle/pedestrian collisions. 17. Document Analysis/Descriptors 18. Availability Statement Bayesian networks
Saskatoon By
"... In presenting this thesis in partial fulfillment of the requirements for a Postgraduate ..."
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In presenting this thesis in partial fulfillment of the requirements for a Postgraduate