  The main goal of this paper is to describe a method for exact inference in
general hybrid Bayesian networks (BNs) (with a mixture of discrete and
continuous chance variables). Our method consists of approximating general
hybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists a
fast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoG
Bayesian networks, and there exists a commercial implementation of this
algorithm. However, this algorithm can only be used for MoG BNs. Some
limitations of such networks are as follows. All continuous chance variables
must have conditional linear Gaussian distributions, and discrete chance nodes
cannot have continuous parents. The methods described in this paper will enable
us to use the LJ algorithm for a bigger class of hybrid Bayesian networks. This
includes networks with continuous chance nodes with non-Gaussian distributions,
networks with no restrictions on the topology of discrete and continuous
variables, networks with conditionally deterministic variables that are a
nonlinear function of their continuous parents, and networks with continuous
chance variables whose variances are functions of their parents.
