A belief‐function model for the representation and the combination of uncertain audit evidence

• Author: Carine Van Den Acker
• Date: 01 September 1999
• Published date: 01 September 1999
• DOI: http://doi.org/10.1002/(SICI)1099-1174(199909)8:3<215::AID-ISAF167>3.0.CO;2-G

A Belief-function Model

for the Representation

and the Combination of

Uncertain Audit Evidence

Carine Van den Acker*

Katholieke Universiteit Leuven, Belgium

Abstract This paper describes a belief-function framework for representing and combin-

ing evidence in financial statement auditing. The use of belief-function theory

for these purposes is not new. A considerable amount of important research

in this respect has been performed mainly by Srivastava and is described in

numerous publications. One of his major achievements is the construction of

a complete framework like the one described in this paper. The framework

that we propose in this text takes a different point of view and addresses a

number of limitations of Srivastava’s framework. Copyright 1999 John

Wiley & Sons, Ltd.

INTRODUCTION

Belief-function theory is one of many formal

theories to represent uncertainty. It became

known as the Dempster–Shafer theory in the

late 1960s and early 1970s and was presented

as ‘a theory of evidence’, aimed at representing

and combining different pieces of uncertain evi-

dence. More than a decade later, the AI com-

munity rediscovered belief-function theory as a

means for representing uncertainty in knowl-

edge-based systems. Today, considerable pro-

gress has been made in its implementation as

well as on issues of interpretation and axio-

matic justification.

The promising flexibility of belief-function

theory for modeling the uncertainty associated

with audit evidence compared to probability

theory was already mentioned in Akresh et

al. (1988). As financial statement auditing is

* Correspondence to: Carine Van den Acker, Depart-

ment of Applied Economic Sciences, Katholieke

Universiteit Leuven, Dekenstraat 2, Leuven 3000,

Belgium

CCC 1055-615X/99/030215-10$17.50

Copyright 1999 John Wiley & Sons, Ltd.

International Journal of Intelligent Systems in Accounting, Finance & Management

Int. J. Intell. Sys. Acc. Fin. Mgmt. 8, 215–224, (1999)

described as ‘the accumulation and evaluation

of evidence . . .’ (Arens and Loebbecke, 1994),

this is indeed the type of problem for which

the belief-function theory was originally

developed. It was mainly Srivastava who did

a lot of research in applying belief-function

theory to financial statement auditing (e.g. Sriv-

astava and Shafer, 1992). He explained how

the use of belief-function theory provides more

flexibility than probability theory and can rep-

resent the true meaning of audit risk. This

framework

1

is of great importance because it

is the first belief-function model for financial

statement auditing and therefore entails many

pioneer developments, including some methods

for the representation of statistical audit evi-

dence. With respect to implementation, signifi-

cant progress was achieved by Shenoy and

Shafer (1986).

Like any model, Srivastava’s model is built

on a number of assumptions and entails some

limitations. To overcome some of these limi-

1

For ease of reference, it will be called ‘Srivastava’s

model’ in the remainder of this text.