Jornal article

Studený M., Vomlel J.

International Journal of Approximate Reasoning

2009

2 (2009)

385-413

0888-613X

RNDr. Milan Studený, DrSc. (ÚTIA - Oddělení matematické teorie rozhodování)

Bayesian network structure, chain graph, essential graph, st

A standard graphical representative of a Bayesian network structure is a special chain graphs, 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 the paper is the proof of correctness of the algorithm.