By Judea Pearl

This summarizes contemporary advances in causal inference and underscores the paradigmatic shifts that has to be undertaken in relocating from conventional statistical research to causal research of multivariate facts. exact 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 equipment which were built for the overview of such claims. those advances are illustrated utilizing a basic thought of causation in response to the Structural Causal version (SCM), which subsumes and unifies different methods to causation, and gives a coherent mathematical starting place for the research of motives and counterfactuals. specifically, the paper surveys the improvement of mathematical instruments for inferring (from a mix of knowledge and assumptions) solutions to 3 forms of causal queries: these approximately (1) the results of strength interventions, (2) chances of counterfactuals, and (3) direct and oblique results (also often called "mediation"). ultimately, 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 gains of either. The instruments are established within the analyses of mediation, factors of results, and possibilities of causation.

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Satisfy the back-door condition) For example, the sets T = {W1, Z3} and Z = {Z3, W2} in Fig. 4 are c-equivalent, because each blocks all back-door paths from X to Y. Similarly, the non-admissible sets T = {Z2} and Z = {W2, Z2} are c-equivalent, since their Markov boundaries are the same (Tm = Zm = {Z2}). In contrast, the sets {W1} and {Z1}, although they block the same set of paths in the graph, are not c-equivalent; they fail both conditions of Theorem 2. Tests for c-equivalence (27) are fairly easy to perform, and they can also be assisted by propensity scores methods.

In other words, any alternative theory needs to evolve as a special case of the “general theory” when restrictions are imposed on either the model, the type of assumptions admitted, or the language in which those assumptions are cast. The structural theory that we use in this survey satisfies the criteria above. It is based on the Structural Causal Model (SCM) developed in (Pearl, 1995, 2000a) which combines features of the structural equation models (SEM) used in economics and social science (Goldberger, 1973, Duncan, 1975), the potential-outcome framework of Neyman (1923) and Rubin (1974), and the graphical models developed for probabilistic reasoning and causal analysis (Pearl, 1988, Lauritzen, 1996, Spirtes, Glymour, and Scheines, 2000, Pearl, 2000a).

Statisticians can no longer ignore the mental representation in which scientists store experiential knowledge, since it is this representation, and the language used to access it that determine the reliability of the judgments upon which the analysis so crucially depends. g. Yx(u) or Zxy. g. ) The expression Yx(u), for example, stands for the value that outcome Y would take in individual u, had treatment X been at level x. If u is chosen at random, Yx is a random variable, and one can talk about the probability that Yx would attain a value y in the population, written P(Yx = y) (see Section 5 for semantics).

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