Department of Statistics, UCLA

The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting distributions on post-action outcomes given a set of measurements. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem, and show applications to sequential decision making.