  Ancestral graphs are a class of graphs that encode conditional independence
relations arising in DAG models with latent and selection variables,
corresponding to marginalization and conditioning. However, for any ancestral
graph, there may be several other graphs to which it is Markov equivalent. We
introduce a simple representation of a Markov equivalence class of ancestral
graphs, thereby facilitating model search. \ More specifically, we define a
join operation on ancestral graphs which will associate a unique graph with a
Markov equivalence class. We also extend the separation criterion for ancestral
graphs (which is an extension of d-separation) and provide a proof of the
pairwise Markov property for joined ancestral graphs.
