Graphical models are graphs with vertices (variables) and edges that encode the conditional independence relations holding among the set of variables of some process. Directed acyclic graphs (DAGs) are commonly used to represent processes in (not exclusively) the biological, econometric, and social sciences. However, there are often many graphs that can encode the same set of conditional independence relations, thus forming a Markov equivalence class. Furthermore, the likelihoods of Markov equivalent graphs are equal. Hence, when performing a model search, it may be more efficient to search across equivalence classes rather than across individual graphs. In this talk we will review how equivalence classes of DAG models are represented and present an equivalence class search across such graphs. We will then focus on situations where some of the variables in the process are latent, and discuss how to represent Markov equivalence classes in this setting.
Group for Research in Decision Analysis