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This paper analyzes irrelevance and independence relations in graphicalmodels associated with convex sets of probability distributions (calledQuasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, Howcan irrelevance/independence relations in Quasi-Bayesian networks be detected,enforced and exploited? This paper addresses these questions through Walley'sdefinitions of irrelevance and independence. Novel algorithms and results arepresented for inferences with the so-called natural extensions using fractionallinear programming, and the properties of the so-called type-1 extensions areclarified through a new generalization of d-separation.

Irrelevance and Independence Relations in Quasi-Bayesian Networks