Epistemic Probability: the Dempster-Shafer theory of evidence

Abstract

We mentioned in Chapter 2 the distinction between subjective and objective probability; two different interpretations of essentially the same mathematical formalism. This sharing of the use of the word ‘probability’ in the naming of both interpretations has led to an unfortunate confounding of two different concepts. The development of the mathematical formalism described in Chapter 2 has strong roots in the statistical analysis of games of chance. However, although Cox’s axioms do provide a justification for the use of Bayesian probability as a measure of belief, it is not necessarily the case that a numerical measure of epistemic belief should be strictly governed by the frequentistic laws of chance. The Dempster-Shafer theory of evidence provides an alternative, more general, model for the assessment of numerical degrees of belief.

The chance governed by an aleatory (random) experiment may or may not coincide with our degrees of belief about the outcome of the experiment. If we know the chances, then we will surely adopt them as our degrees of belief. But if we do not know the chances, then it will be an extraordinary coincidence for our degrees of belief to be equal to them. (Shafer, 1976).