Abstract
A standard graphical representative of a Bayesian network structure
is a special chain graph, known as an essential graph. An alternative
algebraic approach to the mathematical description of this statistical
model uses instead a certain integer-valued vector, known as a standard
imset. We give a direct formula for the translation of any chain
graph describing a Bayesian network structure into the standard imset.
Moreover, we present a two-stage algorithm which makes it possible
to reconstruct the essential graph on the basis of the standard imset.
The core of this paper is the proof of the correctness of the algorithm.
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