A recovery algorithm for chain graphs

The class of chain graphs (CGs) involving both undirected graphs (=Markou networks) and directed acyclic graphs (= Bayesian networks) was introduced in middle eighties for description of probabilistic conditional independence structures. Every class of Markov equivalent CGs (that is, CGs describing the same conditional independence structure) has a natural representative which is called the largest CG. The paper presents a recovery algorithm which on the basis of the conditional independence structure given by a CG (in the form of a dependency model) finds the largest CG representing the corresponding class of Markov equivalent CGs. As a by-product a graphical characterization of graphs which are the largest CGs (for a class of Markov equivalent CGs) is obtained, and a simple algorithm changing every CG into the largest CG of the corresponding equivalence class is given. (C) 1997 Elsevier Science Inc.