Properties of semi-elementary imsets as sums of elementary imsets

Details Properties of semi-elementary imsets as sums of elementary imsets Properties of semi-elementary imsets as sums of elementary imsets

2011-05-30

arxiv.org/abs/1105.6027v1

Journal of Algebraic Statistics 2 (2011) 14-35

Mathematics

Statistics Theory

Scientific paper

We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary imset and prove that all representations are connected by relations among four elementary imsets.

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