On marginalization, collapsibility and precollapsibility.
In Distributions with Given Marginals and
(V. Benes, J. Stepan eds.), Kluwer, Dordrecht 1997, pp. 191-198.
- 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)
G-Markovian 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
- AMS classification 62H17, 68R10
- marginal graph
- undirected graph
pdf copy (converted postscript version) (162kB) is available.
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. 567-578.
- M. Frydenberg:
Marginalization and collapsibility in graphical interaction models.
Annals of Statistics 18 (1990), pp. 790-805.