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The main goal of this paper is to describe a method for exact inference ingeneral hybrid Bayesian networks (BNs) (with a mixture of discrete andcontinuous chance variables). Our method consists of approximating generalhybrid Bayesian networks by a mixture of Gaussians (MoG) BNs. There exists afast algorithm by Lauritzen-Jensen (LJ) for making exact inferences in MoGBayesian networks, and there exists a commercial implementation of thisalgorithm. However, this algorithm can only be used for MoG BNs. Somelimitations of such networks are as follows. All continuous chance variablesmust have conditional linear Gaussian distributions, and discrete chance nodescannot have continuous parents. The methods described in this paper will enableus to use the LJ algorithm for a bigger class of hybrid Bayesian networks. Thisincludes networks with continuous chance nodes with non-Gaussian distributions,networks with no restrictions on the topology of discrete and continuousvariables, networks with conditionally deterministic variables that are anonlinear function of their continuous parents, and networks with continuouschance variables whose variances are functions of their parents.

Inference in Hybrid Bayesian Networks Using Mixtures of Gaussians