Improved Mean and Variance Approximations for Belief Net Responses via Network Doubling
This work provides incremental improvements for researchers and practitioners using Bayesian belief networks to quantify uncertainty in queries, applicable to discrete, continuous, and hybrid networks with complete data.
The paper tackled the problem of approximating the mean and variance of queries in Bayesian belief networks, which quantify uncertainty about conditional probabilities, by developing more accurate approximations using a network doubling technique. The result was demonstrated through empirical studies showing improved effectiveness over existing delta method approximations.
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.