Estimation of Complete Discrete Multivariate Probability Distributions from Scarce Data with Application to Risk Assessment and Fault Detection

Abstract

This paper presents a method of estimating discrete multivariate probability distributions from scarce historical data. Of particular interest is the estimation of the probabilities of rare events. The method is based on maximizing the information entropy subject to equality constraints on the moments of the estimated probability distributions. Two criteria are proposed for optimal selections of the moment functions. The method models nonlinear and nonmonotonic relations with an optimal level of model complexity. Not only does it allow for the estimation of the probabilities of rare events, but, together with Bayesian networks, it also provides a framework to model fault propagation in complex highly interactive systems. An application of this work is in risk assessment and fault detection using Bayesian networks, especially when an accurate first-principles model is not available. The performance of the method is shown through an example.