Confidence Factors, Empiricism and the Dempster-Shafer Theory of Evidence

Abstract

The issue of confidence factors in Knowledge Based Systems has become increasingly important and Dempster-Shafer (DS) theory has become increasingly popular as a basis for these factors. This paper discusses the need for an empirical interpretation of any theory of confidence factors applied to Knowledge Based Systems and describes an empirical interpretation of DS theory suggesting that the theory has been extensively misinterpreted. For the essentially syntactic DS theory, a model is developed based on sample spaces, the traditional semantic model of probability theory. This model is used to show that, if belief functions are based on reasonably accurate sampling or observation of a sample space, then the beliefs and upper probabilities as computed according to DS theory cannot be interpreted as frequency ratios. Since many proposed applications of DS theory use belief functions in situations with statistically derived evidence (Wesley [1]) and seem to appeal to statistical intuition to provide an interpretation of the results as has Garvey [2], it may be argued that DS theory has often been misapplied.