We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
entropy, Bayesian networks, linear inequalities, polyhedral sets, information
94A17, 15A39, 52Bxx