@MISC{Pearl_acausal, author = {Judea Pearl}, title = {A Causal Calculus}, year = {} }

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Abstract

Given an arbitrary causal graph, some of whose nodes are observable and some unobservable, the problem is to determine whether the causal effect of one variable on another can be computed from the joint distribution over the observables and, if the answer is positive, to derive a formula for the causal effect. We introduce a calculus which, using a step by step reduction of probabilistic expressions, derives the desired formulas. 1 1 Introduction Networks employing directed acyclic graphs (DAGs) can be used to provide either 1. an economical scheme for representing conditional independence assumptions and joint distribution functions, or 2. a graphical language for representing causal influences. Although the professed motivation for investigating such models lies primarily in the second category, [Wright, 1921, Blalock, 1971, Simon, 1954, Pearl 1988], causal inferences have been treated very cautiously in the statistical literature [Lauritzen & Spiegelhalter 1988, Cox 1992,...