Pearl's Calculus of Intervention Is Complete

Understand

This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal relationships.

• We first review Pearl's work on this topic [Pearl, 1995], in which several useful graphical criteria are presented.
• Then we present a complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem.
• By exploiting the completeness of this algorithm, we prove that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities.