Propagation in Hybrid Bayesian Networks with Linear Deterministic Variables

This paper extend exacts inference for hybrid Bayesian networks to allow continuous variables with any conditional density functions, discrete variables with continuous parents, and conditionally deterministic continuous variables that are linearly dependent on their continuous parents. We introduce a mixed distribution representation of potentials and derive operations from the method of convolutions in probability theory to determine distributions for linear functions of random variables. Mixtures of truncated exponentials (MTE) potentials are used to approximate probability density functions in the representation so that probability density functions can be easily marginalized in closed form. The Shenoy-Shafer architecture is used to calculate marginals and variables can be marginalized in any order using any join tree structure.