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December 2002 Marginalizing and conditioning in graphical models
Jan T.A. Koster
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Bernoulli 8(6): 817-840 (December 2002).


A class of graphs is introduced which is closed under marginalizing and conditioning. It is shown that these operations can be executed by performing in arbitrary order a sequence of simple, strictly local operations on the graph at hand. The results are based on a simplification of J. Pearl's notion of $d$-separation. As the simplification does not change the separation properties of graphs for which the original $d$-separation concept is applicable (e.g., directed graphs), it constitutes a true generalization of the latter concept to the present class of graphs.


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Jan T.A. Koster. "Marginalizing and conditioning in graphical models." Bernoulli 8 (6) 817 - 840, December 2002.


Published: December 2002
First available in Project Euclid: 9 February 2004

zbMATH: 1011.60026
MathSciNet: MR1963663

Keywords: Gaussian linear equations system , graph , graphical Markov model , linear structural equations system , Markov property , Markov random field , MC graph , non-recursive causal model , separation

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 6 • December 2002
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