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April 2009 Matrix representations and independencies in directed acyclic graphs
Giovanni M. Marchetti, Nanny Wermuth
Ann. Statist. 37(2): 961-978 (April 2009). DOI: 10.1214/08-AOS594


For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.


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Giovanni M. Marchetti. Nanny Wermuth. "Matrix representations and independencies in directed acyclic graphs." Ann. Statist. 37 (2) 961 - 978, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62061
MathSciNet: MR2502657
Digital Object Identifier: 10.1214/08-AOS594

Primary: 62H99
Secondary: 05C50 , 62H05

Keywords: Conditional independence , edge matrix , parent graph , partial closure , partial inversion , separation criteria , stepwise data generating process

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 2 • April 2009
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