Markov Properties for Acyclic Directed Mixed Graphs

We consider acyclic directed mixed graphs, in which directed edges ( x → y ) and bi‐directed edges ( x ↔ y ) may occur. A simple extension of Pearl's d ‐separation criterion, called m ‐separation, is applied to these graphs. We introduce a local Markov property which is equivalent to the global property resulting from the m ‐separation criterion for arbitrary distributions.