  We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs)
to more general types of graphs that describe Markov equivalence classes of
DAGs and/or allow for arbitrarily many hidden variables. We also give easily
checkable necessary and sufficient graphical criteria for the existence of a
set of variables that satisfies our generalized back-door 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 is available in the
R-package pcalg.
