M. Studeny:
On marginalization, collapsibility and precollapsibility.
In Distributions with Given Marginals and
Moment Problems
(V. Benes, J. Stepan eds.), Kluwer, Dordrecht 1997, pp. 191198.
 Abstract
 It is shown that for every undirected graph G over a
finite set N and for every nonempty subset T of
N there exists an undirected graph G(T) over T,
called the marginal graph of G for T, such that the
class of marginal distributions for T of (discrete)
GMarkovian distributions coincides with the class
of G(T)Markovian distributions. An example shows that this
is not true within the framework of strictly positive probability
distributions. However, an analogous positive result holds for
hypergraphs and classes of strictly positive factorizable
distributions.
 AMS classification 62H17, 68R10
 Keywords
 marginal graph
 collapsibility
 marginalization
 undirected graph
 hypergraph

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The results of the paper has a connection to the following works:
 S. Asmussen, D. Edwards: Collapsibility and response
variables in contingency tables. Biometrica 70
(1983), pp. 567578.
 M. Frydenberg:
Marginalization and collapsibility in graphical interaction models.
Annals of Statistics 18 (1990), pp. 790805.