On Separation Criterion and Recovery Algorithm for Chain Graphs
  Chain graphs give a natural unifying point of view on Markov and Bayesian
networks and enlarge the potential of graphical models for description of
conditional independence structures. In the paper a direct graphical separation
criterion for chain graphs, called c-separation, which generalizes the
d-separation criterion for Bayesian networks is introduced (recalled). It is
equivalent to the classic moralization criterion for chain graphs and complete
in sense that for every chain graph there exists a probability distribution
satisfying exactly conditional independencies derivable from the chain graph by
the c-separation criterion. Every class of Markov equivalent chain graphs can
be uniquely described by a natural representative, called the largest chain
graph. A recovery algorithm, which on basis of the (conditional) dependency
model induced by an unknown chain graph finds the corresponding largest chain
graph, is presented.
