  Different directed acyclic graphs (DAGs) may be Markov equivalent in the
sense that they entail the same conditional independence relations among the
observed variables. Meek (1995) characterizes Markov equivalence classes for
DAGs (with no latent variables) by presenting a set of orientation rules that
can correctly identify all arrow orientations shared by all DAGs in a Markov
equivalence class, given a member of that class. For DAG models with latent
variables, maximal ancestral graphs (MAGs) provide a neat representation that
facilitates model search. Earlier work (Ali et al. 2005) has identified a set
of orientation rules sufficient to construct all arrowheads common to a Markov
equivalence class of MAGs. In this paper, we provide extra rules sufficient to
construct all common tails as well. We end up with a set of orientation rules
sound and complete for identifying commonalities across a Markov equivalence
class of MAGs, which is particularly useful for causal inference.
