Bayesian network implementation of Levi's epistemic utility decision theory

Isaac Levi has proposed an epistemic decision rule that requires two convex sets of probability distributions: a set of credal probability distributions that represent a decision agent's state of knowledge, and a set of information-determining distributions that represent the decision agent's assessment of the informational value of various hypotheses. In this paper, we investigate the feasibility of using Bayesian network structures, in which conditional probability distributions are computed using local computations and conditional independence relationships, to implement Levi's decision rule. We find that Bayesian network update algorithms do not in general result in convex sets of distributions; however, Bayesian networks can compute sets of a posteriori extremal distributions from sets of a priori and conditional extremal distributions. We also show that Levi's decision rule gives the same answer when applied to arbitrary sets of credal and information-determining distributions as it gives when applied to the convex closure of those sets of distributions. Thus, implementation of Levi's decision rule using Bayesian network structures is feasible.