Bayesian Networks from the Point of View of Chain Graphs
  AThe paper gives a few arguments in favour of the use of chain graphs for
description of probabilistic conditional independence structures. Every
Bayesian network model can be equivalently introduced by means of a
factorization formula with respect to a chain graph which is Markov equivalent
to the Bayesian network. A graphical characterization of such graphs is given.
The class of equivalent graphs can be represented by a distinguished graph
which is called the largest chain graph. The factorization formula with respect
to the largest chain graph is a basis of a proposal of how to represent the
corresponding (discrete) probability distribution in a computer (i.e.
parametrize it). This way does not depend on the choice of a particular
Bayesian network from the class of equivalent networks and seems to be the most
efficient way from the point of view of memory demands. A separation criterion
for reading independency statements from a chain graph is formulated in a
simpler way. It resembles the well-known d-separation criterion for Bayesian
networks and can be implemented locally.
