Causal Inference by Surrogate Experiments: z-Identifiability.

摘要

We address the problem of estimating the effect of intervening on a set of variables X from experiments on a different set, Z, that is more accessible to manipulation. This problem, which we call z-identifiability reduces to ordinary identifiability when Z = phi and like the latter, can be given syntactic characterization using the do-calculus Pearl, 1995; 2000). We provide a graphical necessary and sufficient condition for z- identifiability for arbitrary sets X,Z, and Y (the out- comes). We further develop a complete algorithm for computing the causal effect of X on Y using information provided by experiments on Z. Finally, we use our results to prove completeness of do- calculus relative to z-identifiability, a result that does not follow from completeness relative to ordinary identifiability.