Implementation of Continuous Bayesian Networks Using Sums of Weighted Gaussians

Bayesian networks provide a method of rep­ resenting conditional independence between random variables and computing the prob­ ability distributions associated with these random variables. In this paper, we ex­ tend Bayesian network structures to compute probability density functions for continuous random variables. We make this extension by approximating prior and conditional den­ sities using sums of weighted Gaussian dis­ tributions and then finding the propagation rules for updating the densities in terms of these weights. We present a simple exam­ ple that illustrates the Bayesian network for continuous variables; this example shows the effect of the network structure and approxi­ mation errors on the computation of densities for variables in the network.