A generalized backdoor criterion

We generalize Pearl's backdoor criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs with or without arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfy our generalized backdoor criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explicit set that fulfills the criterion. We illustrate the results in several examples. R-code will be available in the R-package pcalg.