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17
Causal Reasoning in Graphical Time Series Models
"... We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to the back–door and front–door criteria, are presented and can a ..."
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Cited by 8 (2 self)
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We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to the back–door and front–door criteria, are presented and can also be verified graphically. Computation of the causal effect is derived and illustrated for the linear case. 1
Direct and Indirect Effects of Sequential Treatments
 In: Proc. of the 22nd Conference on Uncertainty in Artificial Intelligence
, 2006
"... In this paper we review the notion of direct and indirect causal effect as introduced by Pearl (2001). We show how it can be formulated without counterfactuals, using regime indicators instead. This allows to consider the natural (in)direct effect as a special case of sequential treatments discussed ..."
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Cited by 7 (3 self)
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In this paper we review the notion of direct and indirect causal effect as introduced by Pearl (2001). We show how it can be formulated without counterfactuals, using regime indicators instead. This allows to consider the natural (in)direct effect as a special case of sequential treatments discussed by Dawid & Didelez (2005) which immediately yields conditions for identifiability as well as a graphical way of checking identifiability. 1
Mendelian Randomisation: Why Epidemiology needs a Formal Language for Causality
"... abstract. For ethical or practical reasons, randomised cotrolled trials are not always an option to test epidemiological hypotheses. Epidemiologists are consequently faced with the problem of how to make causal inferences from observational data, particularly when confounding is present and not full ..."
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Cited by 6 (4 self)
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abstract. For ethical or practical reasons, randomised cotrolled trials are not always an option to test epidemiological hypotheses. Epidemiologists are consequently faced with the problem of how to make causal inferences from observational data, particularly when confounding is present and not fully understood. The method of instrumental variables can be exploited for this purpose in a process known as Mendelian randomisation. However, the approach has not been developed to deal satisfactorily with a binary outcome variable in the presence of confounding. This has not been properly understood in the medical literature. We show that by defining the problem using a formal causal language, the difficulties can be identified and misinterpretations avoided. 1
Graphical models for inference under outcomedependent sampling
 STAT SCI 2010;25:368–87
, 2010
"... We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in casecontrol studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a no ..."
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Cited by 3 (0 self)
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We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in casecontrol studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be made explicit. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples.
On Grangercausality and the effect of interventions in time series
, 2009
"... Abstract. We combine two approaches to causal reasoning. Granger–causality, on the one hand, is popular in fields like econometrics, where randomised experiments are not very common. Instead information about the dynamic development of a system is explicitly modelled and used to define potentially c ..."
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Abstract. We combine two approaches to causal reasoning. Granger–causality, on the one hand, is popular in fields like econometrics, where randomised experiments are not very common. Instead information about the dynamic development of a system is explicitly modelled and used to define potentially causal relations. On the other hand, the notion of causality as effect of interventions is predominant in fields like medical statistics or computer science. In this paper, we consider the effect of external, possibly multiple and sequential, interventions in a system of multivariate time series, the Granger–causal structure of which is taken to be known. We address the following questions: under what assumptions about the system and the interventions does Granger–causality inform us about the effectiveness of interventions, and when does the possibly smaller system of observable times series allow us to estimate this effect? For the latter we derive criteria that can be checked graphically and are similar to the back–door and front–door criteria of Pearl (1995). 1.
Identifying Dynamic Sequential Plans
"... We address the problem of identifying dynamic sequential plans in the framework of causal Bayesian networks, and show that the problem is reduced to identifying causal effects, for which there are complete identification algorithms available in the literature. 1 ..."
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We address the problem of identifying dynamic sequential plans in the framework of causal Bayesian networks, and show that the problem is reduced to identifying causal effects, for which there are complete identification algorithms available in the literature. 1
Identifying Optimal Sequential Decisions
"... We consider conditions that allow us to find an optimal strategy for sequential decisions from a given data situation. For the case where all interventions are unconditional (atomic), identifiability has been discussed by Pearl & Robins (1995). We argue here that an optimal strategy must be conditio ..."
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We consider conditions that allow us to find an optimal strategy for sequential decisions from a given data situation. For the case where all interventions are unconditional (atomic), identifiability has been discussed by Pearl & Robins (1995). We argue here that an optimal strategy must be conditional, i.e. take the information available at each decision point into account. We show that the identification of an optimal sequential decision strategy is more restrictive, in the sense that conditional interventions might not always be identified when atomic interventions are. We further demonstrate that a simple graphical criterion for the identifiability of an optimal strategy can be given. 1
Causal Bounds and Observable Constraints for Nondeterministic Models
"... Conditional independence relations involving latent variables do not necessarily imply observable independences. They may imply inequality constraints on observable parameters and causal bounds, which can be used for falsification and identification. The literature on computing such constraints ofte ..."
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Conditional independence relations involving latent variables do not necessarily imply observable independences. They may imply inequality constraints on observable parameters and causal bounds, which can be used for falsification and identification. The literature on computing such constraints often involve a deterministic underlying data generating process in a counterfactual framework. If an analyst is ignorant of the nature of the underlying mechanisms then they may wish to use a model which allows the underlying mechanisms to be probabilistic. A method of computation for a weaker model without any determinism is given here and demonstrated for the instrumental variable model, though applicable to other models. The approach is based on the analysis of mappings with convex polytopes in a decision theoretic framework and can be implemented in readily available polyhedral computation software. Well known constraints and bounds are replicated in a probabilistic model and novel ones are computed for instrumental variable models without nondeterministic versions of the randomization, exclusion restriction and monotonicity assumptions respectively.
Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality
"... We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with ..."
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We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a nodesplitting transformation. We introduce a new graph, the SingleWorld Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on the set of treatment variables. The nodes on the SWIG are the corresponding counterfactual random variables. We illustrate the theory with a number of examples. Our graphical theory of SWIGs may be used to infer the counterfactual independence relations implied by the counterfactual models developed in Robins (1986, 1987). Moreover, in the absence of hidden variables, the joint distribution of the counterfactuals is identified; the identifying formula is the extended gcomputation formula introduced in (Robins et al., 2004). Although Robins (1986, 1987) did not use DAGs we translate his algebraic results to facilitate understanding of this prior work. An attractive feature of Robins ’ approach is that it largely avoids making counterfactual independence assumptions that are experimentally untestable. As an important illustration we revisit the critique of Robins ’ gcomputation given in (Pearl, 2009, Ch. 11.3.7); we use SWIGs to show that all of Pearl’s claims are either erroneous or based on misconceptions. We also show that simple extensions of the formalism may be used to accommodate dynamic regimes, and to formulate nonparametric structural equation models in which assumptions relating to the absence of direct effects are formulated at the population level. Finally, we show that our graphical theory also naturally arises in the context of an expanded causal Bayesian network in which we are able to observe the natural state of a Potential outcomes are extensively used within Statistics, Political Science, Economics, and Epidemiology for reasoning about causation. Directed acyclic graphs (DAGs) are another formalism used to represent causal systems also
Submitted to the Statistical Science On the Use of Graphical Models for Inference under Outcome Dependent Sampling
"... Abstract. We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case–control studies. Graphical models represent assumptions about the conditional independencies among the variables. By incl ..."
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Abstract. We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case–control studies. Graphical models represent assumptions about the conditional independencies among the variables. By including a node for the sampling indicator, assumptions about sampling processes can be represented. We demonstrate how to read off such graphs whether consistent estimation of the association between exposure and outcome is possible. Moreover, we give sufficient graphical conditions for testing and estimating the causal effect of exposure on outcome. The practical use is illustrated with a number of examples. Key words and phrases: Causal inference; collapsibility; loglinear models; odds ratios; selection bias.. 1.