Convex Bayes Decision Networks.

Abstract

Abstract : This final report describes the results of a project to study the use of Bayesian networks to implement Levi's epistemic utility decision theory. The results of this project can be roughly categorized as falling into one of three areas: (1) implementation of Levi's theory using Bayesian networks, (2) development of Bayesian network updating algorithms for continuous valued network nodes, and (3) application of continuous Bayesian networks to stochastic filtering problems. We found that although Bayesian networks do not preserve the convexity of sets of distributions, Levi's decision theory can still be implemented by computing extremely points in these sets. Also, we developed a method of implementing Bayesian networks containing continuous valued nodes using Gaussian sum approximations; this method is applicable in any context in which a Bayesian network may be applied and, in particular, is not restricted to networks used to implement Levi's theory. Finally we investigated the application of Bayesian networks to stochastic filtering problems and demonstrated this application through a simple angle-only target tracking problem. This report provides an overview of these results, which are fully documented in the PhD dissertation and papers referenced in Section 3.