Causal Analysis in Theory and Practice

October 15, 2006

The validity of G-estimation

Filed under: Book (J Pearl),G-estimation — moderator @ 12:00 pm

From a previous correspondence with Eliezer S. Yudkowsky, Research Fellow, Singularity Institute for Artificial Intelligence, Santa Clara, CA

The following paragraph appears on p. 103, shortly after eq. 3.63 in my copy of Causality:

"To place this result in the context of our analysis in this chapter, we note that the class of semi-Markovian models satisfying assumption (3.62) corresponds to complete DAGs in which all arrowheads pointing to Xk originate from observed variables."

It looks to me like this is a sufficient, but not necessary, condition to satisfy 3.62. It appears to me that the necessary condition is that no confounder exist between any Xi and Lj with i < j and that no confounder exist between any Xi and the outcome variable Y. However, a confounding arc between any Xi and Xj, or a confounding arc between Li and Xj with i <= j, should not render the causal effect non-identifiable. For example, even if a confounding arc exists between X2 and X3 (but no other confounding arcs exist in the model), the causal effect on Y of setting X2=x2 and X3=x3 should be the same as the distribution on Y if we observe x2 and x3.

It is also not necessary that the DAG be complete.

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