A Note on Equivalence Classes of Directed Acyclic Independence Graphs

Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu 1). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits 2 and Madigan and Raftery 4) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.