The belief-function approach to aggregating audit evidence

Abstract

Abstract:In this article, we present the belief-function approach to aggregating audit evidence. The approach uses an evidential network to represent the structure of audit evidence. In turn, it allows us to treat all types of dependencies and relationships among accounts and items of evidence, and thus the approach should help the auditor conduct an efficient and effective audit. Aggregation of evidence is equivalent to propagation of beliefs in an evidential network. The paper describes in detail the three major steps involved in the propagation process. The first step deals with drawing the evidential network representing the connections among variables and items of evidence, based on the experience and judgment of the auditor. We then use the evidential network to determine the clusters of variables over which we have belief functions. The second step deals with constructing a Markov tree from the clusters of variables determined in step one. The third step deals with the propagation of belief functions in the Markov tree. We use a moderately complex example to illustrate the details of the aggregation process. The Belief-Function Approach to Aggregating Audit Evidence. International Journal of Intelligent Systems, 10 (3), 329-356. Publisher's Official Version: <http://onlinelibrary.wiley.com/journal/10.1002/%28ISSN%291098-111X>. Open Access Version: <http://kuscholarworks.ku.edu/dspace/>. Systems, Vol. 10, No. 3, March 1995, pp. 329-356 The Belief-Function Approach to Aggregating Audit Evidence # The Belief-Function Approach to Aggregating Audit Evidence International Journal of Intelligent ABSTRACTIn this article, we present the belief-function approach to aggregating audit evidence. The approach uses an evidential network to represent the structure of audit evidence. In turn, it allows us to treat all types of dependencies and relationships among accounts and items of evidence, and thus the approach should help the auditor conduct an efficient and effective audit.Aggregation of evidence is equivalent to propagation of beliefs in an evidential network. The paper describes in detail the three major steps involved in the propagation process. The first step deals with drawing the evidential network representing the connections among variables and items of evidence, based on the experience and judgment of the auditor. We then use the evidential network to determine the clusters of variables over which we have belief functions.The second step deals with constructing a Markov tree from the clusters of variables determined in step one. The third step deals with the propagation of belief functions in the Markov tree. We use a moderately complex example to illustrate the details of the aggregation process.

On the combination and normalization of interval-valued belief structures☆

“…The Dempster-Shafer theory of evidence (D-S theory or DST for short), which was first developed by Dempster [12] and later extended and refined by Shafer [35], has so far found extensive applications in many areas such as expert systems [4,10,53], diagnosis and reasoning [3,11,[24][25][26]31,33,34,50], pattern classification [8,9,[13][14][15][16][17], information fusion [52], knowledge reduction [58], audit risk assessment [2,22,23,27,[43][44][45][46][47][48][49], multiple attribute decision analysis (MADA) [1,[4][5][6][7]57,59,62,[64][65][66][67][68], environmental impact assessment (EIA) [56], contractor selection …”

Representation of interrelationships among binary variables under dempster-shafer theory of belief functions

“…First, we vacuously (see vacuous extension examples in Srivastava 13 ) extend the belief masses at X 1 and X 2 to the frame of the "weighted average" relationship. Next, we combine the three sets of belief masses at the relationship node by using Dempster's rule of combination and then marginalize (see marginalization examples in Srivastava 13 ) them to the variable Z. The frame of the relationship is defined as = ({zx 1 x 2 ,…”

Auditors’ Evaluations of Uncertain Audit Evidence: Belief Functions versus Probabilities

“…Almost all of the work in belief function evidential networks (for example, Srivastava and Shafer [2], Srivastava [3], [4] and Mock, Wright and Srivastava [12]) has been theoretical and not empiricaL Tbe theoretical arguments for using belief function evidential networks have been strong and intuitively appealing, but no empirical testing of the use of belief functions in an audit setting has been performed. This paper addresses that need for empirical testing.…”

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AbstractRecently, Shafer and Srivastava [1], Srivastava and Shafer [2], Srivastava [3]- [4], and Van den Acker [5] have identified appealing features of belief function evidential networks. These networks can express the support that audit evidence provides for assertions, accounts and fmancial statements.

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