M. Studeny:
Bayesian networks from the point of view of chain graphs.
In Uncertainty in Artificial Intelligence.
Proceedings of the 14th Conference
(G. F. Cooper, S. Moral eds.), Morgan Kaufmann, San Francisco 1998, pp. 496503.
 Abstract
 The 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 wellknown dseparation criterion for Bayesian networks
and can be implemented 'locally'.
 AMS classification 68T30, 62H05
 Keywords
 Bayesian network
 chain graph
 Markov equivalence
 factorization formula
 superactive route
 cseparation

A
pdf copy (343kB) is available.
The paper builds on the following works:
 M. Frydenberg: The chain graph Markov property.
Scandinavian Journal of Statistics
17 (1990), n. 3, pp. 333353.
 S.A. Andersson, D. Madigan, M.D. Perlman:
On the Markov equivalence of chain graphs, undirected graphs and
acyclic digraphs. Scandinavian Journal of Statistics
24 (1997), n. 3, pp. 81102.
 M. Studeny and R. R. Bouckaert:
On chain graph models for description of conditional
independence structures.
The Annals of Statistics
26 (1998), n. 4, pp. 14341495.
 M. Volf and M. Studeny:
A graphical characterization of the largest chain graphs.
International Journal of Approximate Reasoning
20 (1999), pp. 209236.