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

TL;DR

This paper critiques the Dempster-Shafer theory of evidence, emphasizing the need for an empirical interpretation and highlighting common misapplications in statistical contexts within Knowledge Based Systems.

Contribution

It provides an empirical interpretation of DS theory, demonstrating that belief functions cannot be interpreted as frequency ratios when based on sampling.

Findings

Belief functions are not frequency ratios under sampling.

Many applications of DS theory misuse the belief functions in statistical contexts.

The paper develops a model based on sample spaces to interpret DS theory empirically.

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 lnterpretatlon of any theory of confidence factors applied to Knowledge Based Systems and describes an empirical lnterpretatlon 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 lnterpretatlon of the results as has Garvey [2], it may be argued that DS theory has often been misapplied.