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When a hybrid Bayesian network has conditionally deterministic variables withcontinuous parents, the joint density function for the continuous variablesdoes not exist. Conditional linear Gaussian distributions can handle such caseswhen the continuous variables have a multi-variate normal distribution and thediscrete variables do not have continuous parents. In this paper, operationsrequired for performing inference with conditionally deterministic variables inhybrid Bayesian networks are developed. These methods allow inference innetworks with deterministic variables where continuous variables may benon-Gaussian, and their density functions can be approximated by mixtures oftruncated exponentials. There are no constraints on the placement of continuousand discrete nodes in the network.

Hybrid Bayesian Networks with Linear Deterministic Variables