A RECOVERY ALGORITHM FOR CHAIN GRAPHS

The class of chain graphs (CGs) involving both undirected graphs (=Mar kou networks) and directed acyclic graphs (= Bayesian networks) was in troduced in middle eighties for description of probabilistic condition al 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 pres ents a recovery algorithm which on the basis of the conditional indepe ndence structure given by a CG (in the form of a dependency model) fin ds the largest CG representing the corresponding class of Markov equiv alent CGs. As a by-product a graphical characterization of graphs whic h are the largest CGs (for a class of Markov equivalent CGs) is obtain ed, and a simple algorithm changing every CG into the largest CG of th e corresponding equivalence class is given. (C) 1997 Elsevier Science Inc.