Stable local computation with conditional Gaussian distributions

This article describes a propagation scheme for Bayesian networks with conditional Gaussian distributions that does not have the numerical weaknesses of the scheme derived in Lauritzen (Journal of the American Statistical Association 87: 1098-1108, 1992). The propagation architecture is that of Lauritzen and Spiegelhalter (Journal of the Royal Statistical Society, Series B 50: 157-224, 1988). In addition to the means and variances provided by the previous algorithm, the new propagation scheme yields full local marginal distributions. The new scheme also handles linear deterministic relationships between continuous variables in the network specification. The computations involved in the new propagation scheme are simpler than those in the previous scheme and the method has been implemented in the most recent version of the HUGIN software