Matrix representations and independencies in directed acyclic graphs

Details Matrix representations and independencies in directed acyclic graphs Matrix representations and independencies in directed acyclic graphs

2009-04-02

arxiv.org/abs/0904.0333v1

Annals of Statistics 2009, Vol. 37, No. 2, 961-978

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/08-AOS594 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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