  A Bayesian belief network models a joint distribution with an directed
acyclic graph representing dependencies among variables and network parameters
characterizing conditional distributions. The parameters are viewed as random
variables to quantify uncertainty about their values. Belief nets are used to
compute responses to queries; i.e., conditional probabilities of interest. A
query is a function of the parameters, hence a random variable. Van Allen et
al. (2001, 2008) showed how to quantify uncertainty about a query via a delta
method approximation of its variance. We develop more accurate approximations
for both query mean and variance. The key idea is to extend the query mean
approximation to a "doubled network" involving two independent replicates. Our
method assumes complete data and can be applied to discrete, continuous, and
hybrid networks (provided discrete variables have only discrete parents). We
analyze several improvements, and provide empirical studies to demonstrate
their effectiveness.

Artificial Intelligence