Prediction and experimental design with graphical causal models

Abstract: "We unify two contemporary theoretical frameworks for representing causal dependencies. Directed graphical models were introduced and developed by Kiiveri, Speed, Wermuth, Lauritzen, Pearl and others. Rubin introduced a framework for analyzing the relation between the conditional probability of Y on X and the distribution Y would have if X were forced to have a particular value. Pratt and Schlaifer have extended Rubin's analysis to offer sufficient 'counterfactual' conditions for the conditional distribution of Y on Z, X=x to equal the conditional distribution of Y on Z when all units in the population are forced to have that value of X. Using two axioms for directed graphical causal models, we obtain rigorous derivations of claims given by Rubin and by Pratt and Schlaifer, and we give general characterizations in terms of causal structure -- represented by directed graphs -- for Pratt and Schlaifer's notions of the 'observability of a law' and the 'observability of a law with concomitants.' Results obtained in the Rubin framework are generalized, and some relevant sampling properties of graphical causal models are obtained."