Inference in hybrid Bayesian networks with mixtures of truncated exponentials

An important class of hybrid Bayesian networks are those that have conditionally de-terministic variables (a variable that is a deterministic function of its parents). In this case, if some of the parents are continuous, then the joint density function does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when the deter-ministic function is linear and continuous variables are normally distributed. In this paper, we develop operations required for performing inference with conditionally deterministic variables using relationships derived from joint cumulative distribution functions (CDF’s). These methods allow inference in networks with deterministic variables where continuous variables are non-Gaussian.