Confidence Interval of Bayesian Network and Global Sensitivity Analysis

A Bayesian network represents a causal relationship among random variables using conditional probabilities. Because of limited resources and sampling uncertainty, the estimated probabilities have both aleatory randomness and epistemic uncertainty. In this paper, two approaches are used to estimate the confidence intervals of component- and system-level probabilities. The first approach uses an analytical method, where a normal distribution is assumed for the component- and system-level probabilities. Another approach is the bootstrap method, which uses resampling to build a distribution of the probabilities. Global sensitivity is analyzed as well to identify the component-level probability that most significantly affects the uncertainty in the system level. It is shown that the confidence intervals of system probability can be effectively narrowed by reducing sampling uncertainty in the most significant component.