Conditional Independence Structures for Mixed Graphs

In this talk we describe several classes of graphs used in the literature of graphical Markov models to capture the conditional independence structure. These range from the simple undirected and directed acyclic graphs to the more complex classes of mixed graphs with three types of edges. We focus on a unifying interpretation of independence structure for these graphs, in particular an interpretation of a missing edge known as a pairwise Markov property and a criterion for reading off arbitrary conditional independencies known as the global Markov property. We prove the equivalence of pairwise and global Markov properties under certain conditions.