Integrating statistical audit evidence with belief function theory

Abstract

This paper proposes a method for integrating statistical audit evidence (sampling evidence) with belief function theory. Our point of view is the interpretation of belief-function theory as a theory of evidence. The need for integration is urged by the suitability of belief function theory to model the auditor's thought process of collecting and aggregating evidence on the one hand, and the frequent use of both statistical and non-statistical evidence in auditing practice on the other hand. The method we propose is of a general nature and is motivated by the analogy with the way in which sampling evidence is used in auditing practice. Its properties are briefly discussed from the point view of probability theory, though the main part of the paper concentrates on our proposed method and a comparison with Shafer's (Shafer, 1976). Several examples are used to demonstrate both methods' properties.