Minimal separators in dependency structures: Properties and identification.

This paper considers some properties of (locally) minimal separators in oriented graphical dependency models, i.e., in Bayesian networks, Gaussian networks, and hybrid networks. Statements and rules are inferred from the criterion of d-separation and acyclic property of digraph. Necessary conditions are established that should be satisfied by members of (locally) minimal separators. Patterns of evidences are found that allow one to identify the presence or absence of an edge without an extensive search for a separator. These means facilitate the efficient inference of a model structure with the help of constraint-based algorithms