By Judea Pearl

This summarizes fresh 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. specified 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 constructed for the overview of such claims. those advances are illustrated utilizing a basic concept of causation according to the Structural Causal version (SCM), which subsumes and unifies different methods to causation, and offers a coherent mathematical beginning for the research of motives and counterfactuals. particularly, the paper surveys the improvement of mathematical instruments for inferring (from a mix of information and assumptions) solutions to 3 varieties of causal queries: these approximately (1) the results of capability 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 offers instruments for a symbiotic research that makes use of the robust beneficial properties of either. The instruments are verified within the analyses of mediation, factors of results, and possibilities of causation.

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**Sample text**

In general, it can be shown (Pearl, 2000a, p. 73) that, whenever the graph is Markovian the post-interventional distribution P(Y = y|do(X = x)) is given by the following expression: (24) where T is the set of direct causes of X (also called “parents”) in the graph. This allows us to write (23) directly from the graph, thus skipping the algebra that led to (23). It further implies that, no matter how complicated the model, the parents of X are the only variables that need to be measured to estimate the causal effects of X.

Thus, in our example, the complete model of a symptom and a disease would be written as in Fig. 1: The diagram encodes the possible existence of (direct) causal influence of X on Y, and the absence of causal influence of Y on X, while the equations encode the quantitative relationships among the variables involved, to be determined from the data. The parameter β in the equation is called a “path coefficient” and it quantifies the (direct) causal effect of X on Y; given the numerical values of β and UY, the equation claims that, a unit increase for X would result in β units increase of Y regardless of the values taken by other variables in the model, and regardless of whether the increase in X originates from external or internal influences.

Our problem is to select a subset of these factors for measurement and adjustment, namely, that if we compare treated vs. untreated subjects having the same values of the selected factors, we get the correct treatment effect in that subpopulation of subjects. Such a set of factors is called a “sufficient set” or “admissible set” for adjustment. , 1999, Pearl, 1998) for review). View larger versionFigure 4: Markovian model illustrating the back-door criterion. Error terms are not shown explicitly.

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