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31
Axioms of Causal Relevance
 Artificial Intelligence
, 1996
"... This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization of informational irr ..."
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Cited by 54 (15 self)
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This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance, as in "Learning X will not alter our belief in Y , once we know Z." Two versions of causal irrelevance are analyzed, probabilistic and deterministic. We show that, unless stability is assumed, the probabilistic definition yields a very loose structure, that is governed by just two trivial axioms. Under the stability assumption, probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs. Under the deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs, with the exception of transitivity. We compare our formalism to that of [Lewis, 1973], and offer a graphical method of proving theorems abou...
An Axiomatic Characterization of Causal Counterfactuals
, 1998
"... This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedback ..."
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Cited by 47 (19 self)
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This paper studies the causal interpretation of counterfactual sentences using a modifiable structural equation model. It is shown that two properties of counterfactuals, namely, composition and effectiveness, are sound and complete relative to this interpretation, when recursive (i.e., feedbackless) models are considered. Composition and effectiveness also hold in Lewis's closestworld semantics, which implies that for recursive models the causal interpretation imposes no restrictions beyond those embodied in Lewis's framework. A third property, called reversibility, holds in nonrecursive causal models but not in Lewis's closestworld semantics, which implies that Lewis's axioms do not capture some properties of systems with feedback. Causal inferences based on counterfactual analysis are exemplified and compared to those based on graphical models.
Causal diagrams
, 2008
"... Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probabil ..."
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Cited by 23 (2 self)
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Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probability models, enabling use of graph theory in probabilistic inference, and allowing easy deduction of independence conditions implied by the assumptions. They can also be used as a formal tool for causal inference, such as predicting the effects of external interventions. Given that the diagram is correct, one can see whether the causal effects of interest (target effects, or causal estimands) can be estimated from available data, or what additional observations are needed to validly estimate those effects. One can also see how to represent the effects as familiar standardized effect measures. The present article gives an overview of: (1) components of causal graph theory; (2) probability interpretations of graphical models; and (3) methodologic implications of the causal and probability structures encoded in the graph, such as sources of bias and the data needed for their control.
Identifying the consequences of dynamic treatment strategies
, 2005
"... We formulate the problem of learning and comparing the effects of dynamic treatment strategies in a probabilistic decisiontheoretic framework, and in particular show how Robins’s “Gcomputation ” formula arises naturally. Careful attention is paid to the mathematical and substantive conditions nece ..."
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Cited by 18 (10 self)
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We formulate the problem of learning and comparing the effects of dynamic treatment strategies in a probabilistic decisiontheoretic framework, and in particular show how Robins’s “Gcomputation ” formula arises naturally. Careful attention is paid to the mathematical and substantive conditions necessary to justify use of this formula. Probabilistic influence diagrams are used to simplify manipulations. We compare our approach with formulations based on causal DAGs and on potential response models. Some key words and phrases: Causal inference; Gcomputation; Influence diagram; Observational study; Potential response; Sequential decision theory; Stability. 1
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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Cited by 14 (0 self)
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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, ...
Instrumental variables and inverse probability weighting for causal inference from longitudinal observational studies
, 2004
"... ..."
Time series estimation of the effects of natural experiments
 Journal of Econometrics
, 2006
"... Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We d ..."
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Cited by 7 (6 self)
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Abstract This paper investigates methods for estimating the effects of natural experiments, especially those created by an intervention or structural change occurring at a specific point in time, such as a government policy intervention, a merger, or the formation or disintegration of a cartel. We draw on the extensive literature of
Beware of the DAG!
 NIPS 2008 WORKSHOP ON CAUSALITY
, 2008
"... Directed acyclic graph (DAG) models are popular tools for describing causal relationships and for guiding attempts to learn them from data. In particular, they appear to supply a means of extracting causal conclusions from probabilistic conditional independence properties inferred from purely observ ..."
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Cited by 7 (0 self)
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Directed acyclic graph (DAG) models are popular tools for describing causal relationships and for guiding attempts to learn them from data. In particular, they appear to supply a means of extracting causal conclusions from probabilistic conditional independence properties inferred from purely observational data. I take a critical look at this enterprise, and suggest that it is in need of more, and more explicit, methodological and philosophical justification than it typically receives. In particular, I argue for the value of a clean separation between formal causal language and intuitive causal assumptions.
2007): “Defining and estimating intervention effects for groups that will develop an auxiliary outcome
 Statistical Science
"... Abstract. It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropri ..."
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Cited by 7 (0 self)
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Abstract. It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropriately adjusts for variables affected by treatment and so is biased. We consider several appropriate ways to formalize the effects: principal stratification, stratification on a single potential auxiliary variable, stratification on an observed auxiliary variable and stratification on expected levels of auxiliary variables. We then outline identifying assumptions for each type of estimand. We evaluate the utility of these estimands and estimation procedures for decision making and understanding causal processes, contrasting them with the concepts of direct and indirect effects. We motivate our development with examples from nephrology and cancer screening, and use simulated data and real data on cancer screening to illustrate the estimation methods. Key words and phrases: Causality, direct effects, interaction, effect modification, bias, principal stratification.
Adjustments and their Consequences – Collapsibility Analysis using Graphical Models
"... We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjus ..."
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Cited by 5 (1 self)
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We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association of two variables when that association is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a potential source of bias in estimating causal effects, and some additional special cases useful for casecontrol studies, cohort studies with loss, and trials with noncompliance (nonadherence).