By Judea Pearl
This summarizes contemporary advances in causal inference and underscores the paradigmatic shifts that needs to be undertaken in relocating from conventional statistical research to causal research of multivariate info. precise emphasis is put on the assumptions that underlie all causal inferences, the languages utilized in formulating these assumptions, the conditional nature of all causal and counterfactual claims, and the tools which have been built for the review of such claims. those advances are illustrated utilizing a normal thought of causation in line with the Structural Causal version (SCM), which subsumes and unifies different ways to causation, and gives a coherent mathematical beginning for the research of factors and counterfactuals. specifically, the paper surveys the improvement of mathematical instruments for inferring (from a mix of information and assumptions) solutions to 3 kinds of causal queries: these approximately (1) the consequences of capability interventions, (2) chances of counterfactuals, and (3) direct and oblique results (also referred to as "mediation"). eventually, the paper defines the formal and conceptual relationships among the structural and potential-outcome frameworks and provides instruments for a symbiotic research that makes use of the powerful good points of either. The instruments are established within the analyses of mediation, reasons of results, and chances of causation.
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Extra resources for An Introduction to Causal Inference
More sophisticated estimation techniques are the “marginal structural models” of (Robins, 1999), and the “propensity score” method of (Rosenbaum and Rubin, 1983) which were found to be particularly useful when dimensionality is high and data are sparse (see Pearl (2009b, pp. 348–52)). , (Rubin, 2007, 2009)), propensity score methods are merely efficient estimators of the right hand side of (25); they entail the same asymptotic bias, and cannot be expected to reduce bias in case the set S does not satisfy the back-door criterion (Pearl, 2000a, 2009c,d).
The definition, axiomatization and algorithmization of counterfactuals and joint probabilities of counterfactuals Reducing the evaluation of “effects of causes,” “mediated effects,” and “causes of effects” to an algorithmic level of analysis. Solidifying the mathematical foundations of the potential-outcome model, and formulating the counterfactual foundations of structural equation models. Demystifying enigmatic notions such as “confounding,” “mediation,” “ignorability,” “comparability,” “exchangeability (of populations),” “superexogeneity” and others within a single and familiar conceptual framework.
2(a), for example, encodes seven causal assumptions, each corresponding to a missing arrow or a missing double-arrow between a pair of variables. None of those assumptions is testable in isolation, yet the totality of all those assumptions implies that Z is unassociated with Y in every stratum of X. Such testable implications can be read off the diagrams using a graphical criterion known as d-separation (Pearl, 1988). View larger versionFigure 2: (a) The diagram associated with the structural model of Eq.