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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 23 (8 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.
Statistics and Causal Inference: A Review
, 2003
"... This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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 assump ..."
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Cited by 12 (6 self)
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This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.
Causal Inference in the Health Sciences: A Conceptual Introduction
 Health Services and Outcomes Research Methodology
, 2001
"... This paper provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivari ..."
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Cited by 7 (0 self)
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This paper provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper 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 underlie all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, corrections for noncompliance, and a symbiosis between counterfactual and graphical methods of analysis.
Inequality constraints in causal models with hidden variables
 In Proceedings of the Seventeenth Annual Conference on Uncertainty in Artificial Intelligence (UAI06
, 2006
"... We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects that are not directly measured in randomized experiments. W ..."
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Cited by 7 (4 self)
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We present a class of inequality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network, in which some of the variables remain unmeasured. We derive bounds on causal effects that are not directly measured in randomized experiments. We derive instrumental inequality type of constraints on nonexperimental distributions. The results have applications in testing causal models with observational or experimental data. 1
Analysis of the Binary Instrumental Variable Model
"... We give an explicit geometric characterization of the set of distributions over counterfactuals that are compatible with a given observed joint distribution fortheobservablesinthebinary instrumental variable model. This paper will appear as Chapter 25 in Heuristics, Probability and Causality: A Trib ..."
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Cited by 1 (0 self)
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We give an explicit geometric characterization of the set of distributions over counterfactuals that are compatible with a given observed joint distribution fortheobservablesinthebinary instrumental variable model. This paper will appear as Chapter 25 in Heuristics, Probability and Causality: A Tribute to Pearl’s seminal work on instrumental variables [Chickering andPearl1996;BalkeandPearl 1997] for discrete data represented a leap forwards in terms of understanding: Pearl showed that, contrary to what many had supposed based on linear models, in the discrete case the assumption that a variable was an instrument could be subjected to empirical test. In
Causal inference in statistics:
, 2009
"... Abstract: 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 under ..."
Abstract
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Abstract: 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.
The geometry of causal probability trees that are algebraically constrained
"... In this chapter we show how algebraic geometry can be used to define and then analyse the properties of certain important classes of discrete probability models described through probability trees. Our aim is to show how much wider classes of discrete statistical models than have been considered pre ..."
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In this chapter we show how algebraic geometry can be used to define and then analyse the properties of certain important classes of discrete probability models described through probability trees. Our aim is to show how much wider classes of discrete statistical models than have been considered previously have a useful algebraic formulation and unlike its competitors this class is closed under discovery of arbitrary marginal distributions. We proceed to illustrate how the identifiability of certain causal functions can be articulated and analysed within this framework which generalises the causal Bayesian network formulation. We note that as with causal Bayesian networks the most convenient polynomial parametrisation is one that is based on conditional rather than marginal probabilities. In Section 1 we introduce the probability tree representation of a discrete model and show that discrete Bayesian networks and some of their recent generalisations are special subclasses of these models. We then introduce an algebraic representation of important classes of probability tree models called algebraic constraint models (ACTs). In Section 3 we proceed to examine how ACTs are closed under the discovery of the marginal distribution of a random variable measurable with respect to the path sigma algebra of its underlying probability tree. Probability tree representations are especially useful to specify and study the implications of certain causal hypotheses. In Sections 4 and 5 we relate these causal models to ACTs and give a formal discussion of the conditional probability graphs of discrete models that can also be expressed as Bayesian networks. In Section 6 we illustrate these ideas from the perspective of a simple modelling context. 1 The algebra of probability trees Begin by considering a finite discrete probability space whose atomic events are given by the N root to leaf paths on a probability tree T = (V (T), E(T)), CRiSM Paper No. 0609, www.warwick.ac.uk/go/crism
Statistics and Causal Inference: A Review Judea Pearl ∗
"... This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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 assumptio ..."
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This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.
© Institute of Mathematical Statistics, 2010 Assumptions of IV Methods for
"... Abstract. Instrumental variable (IV) methods are becoming increasingly popular as they seem to offer the only viable way to overcome the problem of unobserved confounding in observational studies. However, some attention has to be paid to the details, as not all such methods target the same causal p ..."
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Abstract. Instrumental variable (IV) methods are becoming increasingly popular as they seem to offer the only viable way to overcome the problem of unobserved confounding in observational studies. However, some attention has to be paid to the details, as not all such methods target the same causal parameters and some rely on more restrictive parametric assumptions than others. We therefore discuss and contrast the most common IV approaches with relevance to typical applications in observational epidemiology. Further, we illustrate and compare the asymptotic bias of these IV estimators when underlying assumptions are violated in a numerical study. One of our conclusions is that all IV methods encounter problems in the presence of effect modification by unobserved confounders. Since this can never be ruled out for sure, we recommend that practical applications of IV estimators be accompanied routinely by a sensitivity analysis.