  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.
