Bayesian Integration of Uncertain and Conflicting Evidence

Abstract

Often numeric values assigned to the probability of some fact or rule axe only vague estimates. Using Bayesian analysis the probabilities themselves may be treated as random quantities whose accuracy can be described by a second order probability measure. For the probabilities of consequences a posterior distribution may be derived, which reflects the uncertainty of the input probabilities. The algorithm discussed in this paper is based on an approximate sample representation of the basic probabilities. This sample is continuously modified by a stochastic simulation procedure, the Metropolis algorithm, and the sequence of successive samples yields the desired posterior distribution. The procedure is able to pool inconsistent probabilities according to their reliability and is applicable to general inference networks with arbitrary structure including loops and cycles. The properties of the approach axe demonstrated by some numerical experiments.