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On Marginalization, Collapsibility and Precollapsibility

In: Distributions with given Marginals and Moment Problems

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  • M. Studený

    (Academy of Sciences of Czech Republic, Institute of Information Theory and Automation)

Abstract

It is shown that for every undirected graph G over a finite set N and for every nonempty T ⊂ 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 distributions.

Suggested Citation

  • M. Studený, 1997. "On Marginalization, Collapsibility and Precollapsibility," Springer Books, in: Viktor Beneš & Josef Štěpán (ed.), Distributions with given Marginals and Moment Problems, pages 191-198, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5532-8_22
    DOI: 10.1007/978-94-011-5532-8_22
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