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INTRODUCTION

The theory of convex sets of distributions, variously called the theory of imprecise probabilities [28] or Quasi-Bayesian theory [14], is appropriate for robustness analysis [1,19,29] and for representation of imprecise/incomplete beliefs and opinions [20].

Quasi-Bayesian networks are multivariate structures that represent convex sets of joint distributions by directed acyclic graphs [3,9,27]. The key technical problem in Quasi-Bayesian networks is how to detect, enforce and exploit irrelevance and independence relations. The goal of this paper is to present novel results and algorithms that address these questions. This paper adopts Walley's definitions of irrelevance and independence, and investigates two different methods to generate inferences from Quasi-Bayesian network: inferences from type-1 extensions (Section 4), and inferences from natural extensions (Section 5).

The overall contribution of this paper is a theory of locally defined Quasi-Bayesian networks that display the same flexibility and representational power of standard Bayesian networks. The results in this paper state the conditions that must be required or enforced to express judgements of irrelevance/independence through Quasi-Bayesian networks.



Fabio Gagliardi Cozman
1998-07-03