Arc reversals in hybrid Bayesian networks with deterministic variables

This article discusses arc reversals in hybrid Bayesian networks with deterministic variables. Hybrid Bayesian networks contain a mix of discrete and continuous chance variables. In a Bayesian network representation, a continuous chance variable is said to be deterministic if its conditional distributions have zero variances. Arc reversals are used in making inferences in hybrid Bayesian networks and influence diagrams. We describe a framework consisting of potentials and some operations on potentials that allows us to describe arc reversals between all possible kinds of pairs of variables. We describe a new type of conditional distribution function, called partially deterministic, if some of the conditional distributions have zero variances and some have positive variances, and show how it can arise from arc reversals.