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A Bayesian belief network models a joint distribution with an directedacyclic graph representing dependencies among variables and network parameterscharacterizing conditional distributions. The parameters are viewed as randomvariables to quantify uncertainty about their values. Belief nets are used tocompute responses to queries; i.e., conditional probabilities of interest. Aquery is a function of the parameters, hence a random variable. Van Allen etal. (2001, 2008) showed how to quantify uncertainty about a query via a deltamethod approximation of its variance. We develop more accurate approximationsfor both query mean and variance. The key idea is to extend the query meanapproximation to a "doubled network" involving two independent replicates. Ourmethod assumes complete data and can be applied to discrete, continuous, andhybrid networks (provided discrete variables have only discrete parents). Weanalyze several improvements, and provide empirical studies to demonstratetheir effectiveness.

Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling