  This paper analyzes irrelevance and independence relations in graphical
models associated with convex sets of probability distributions (called
Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How
can irrelevance/independence relations in Quasi-Bayesian networks be detected,
enforced and exploited? This paper addresses these questions through Walley's
definitions of irrelevance and independence. Novel algorithms and results are
presented for inferences with the so-called natural extensions using fractional
linear programming, and the properties of the so-called type-1 extensions are
clarified through a new generalization of d-separation.
