Credal networks

This paper presents a complete theory of credal networks, structures that a ssociate convex sets of probability measures with directed acyclic graphs. Credal networks are graphical models for precise/imprecise beliefs. The mai n contribution of this work is a theory of credal networks that displays as much flexibility and representational power as the theory of standard Baye sian networks. Results in this paper show how to express judgements of irre levance and independence, and how to compute inferences in credal networks. A credal network admits several extensions-several sets of probability mea sures comply with the constraints represented by a network. Two types of ex tensions are investigated. The properties of strong extensions are clarifie d through a new generalization of d-separation, and exact and approximate i nference methods are described for strong extensions. Novel results are pre sented for natural extensions, and linear fractional programming methods ar e described for natural extensions. The paper also investigates credal netw orks that are defined globally through perturbations of a single network. ( C) 2000 Elsevier Science B.V. All rights reserved.