On Separation Criterion and Recovery Algorithm for Chain Graphs

Chain graphs {CGs) give a natural unifying point of view on Markov and Bayesian net­ works and enlarge the potential of graphi­ cal models for description of conditional in­ dependence structures. In the paper a di­ rect graphical separation criterion for CGs which generalizes the d-separation criteri­ on for Bayesian networks is introduced (re­ called). It is equivalent to the classic mo _ r­ alization criterion for CGs and complete m the sense that for every CG there exists a probability distribution satisfying exactly in­ dependencies derivable from the CG by the separation criterion. Every class of Markov e­ quivalent CGs can be uniquely described by a natural representative, called the largest CG. A recovery algorithm, which on basis of the (conditional) dependency model given by a CG finds the corresponding largest CG, is p­