Subjective inference with multiple evidence

摘要

The analysis of a number of pieces of evidence supporting a single hypothesis is undertaken within a Bayesian framework. A new relevance definition is introduced that takes advantage of the linear relationship existing between the posterior probability of the hypothesis and that of a single piece of evidence. Two different simplifying assumptions lead to expressions for the posterior probability of the hypothesis based on revised probabilities of all the evidence. The first assumption is one of mutual independence of each piece of evidence from all other evidence. The second assumption is one of independence of the relevance of each piece of evidence to the hypothesis from the probabilities of the remaining evidence. Most important, expressions for upper bounds on the input relevances are given that guarantee the consistency of the resulting posterior for the hypothesis.