In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the possibility of local computation from the axioms. Next, we describe a propagation scheme for computing marginals of a valuation when we have a factorization of the valuation on a hypertree. Finally we show how the problem of computing marginals of joint probability distributions and joint belief functions fits the general framework. 1.

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This article performs two types of analysis using Dempster-Shafer theory of belief functions for evidential reasoning. The first analysis deals with the impact of the structure of audit evidence on the overall belief at each variable in the network, variables being the account balance to be audited, the related transaction streams, and the associated audit objectives. The second analysis deals with the impact of the relationship (logical "and" and "algebraic relationship") among various variables in the network on the overall belief. For our first analysis, we change the evidential structure from a network to a tree and determine its impact.

Willingham for valuable comments on an earlier version of the article.

The main goal of this paper is to demonstrate how the theory of belief functions

The main purpose of this article is to show how one can integrate statistical evidence from attribute sampling with non-statistical evidence within the Dempster-Shafer belief function framework. In particular, the article shows: (1) how to determine the sample size in attribute sampling to obtain a desired level of belief that the true attribute occurrence rate of the population lies in a given interval; (2) what level of belief is obtained for a specified interval given the sample result; and (3) how to integrate non-statistical evidence with the statistical evidence arising from the attribute sampling. These issues are important to the auditor and therefore we use auditing examples to illustrate the process. As intuitively expected, we find that the sample size increases as the desired level of belief in the interval increases. In evaluating the sample results, we again find results that are intuitively appealing. For example, provided the sample occurrence rate falls in the interval B for a given number of occurrences of the attribute, we find that the belief in B, Bel(B), increases as the sample size increases. However, if the sample occurrence rate falls outside of the interval then Bel(B) is zero. Note that, in general, both Bel(B) and Bel(notB) are zero when the sample occurrence rate falls at the end points of the interval. These results extend similar results already available for variables sampling. However, the auditor faces an additional

Acknowledgements: We would like to thank the audit firm for making their audit work papers available for the study. We sincerely appreciate the help provided by the audit manager and for suggestions provided by Mike Ettredge, Greg Freix, Prakash Shenoy, and participants in AIS workshops at the University of Kansas and the 6th Annual INFORMS Conference on Information Systems and Technology. In addition, the authors would like to thank Drs. Jay F.

The purpose of this chapter is to demonstrate the use of evidential reasoning approach under Dempster-Shafer (D-S) theory of belief functions to analyze revealed causal maps. Revealed causal mapping (RCM) technique, as applied in this chapter, is a qualitative method used to develop or extend understanding of a phenomenon within a specific context. The map can be used to develop models, either as grounded theory or evocative theory building. The example referenced in this study used interview data as the primary source in the RCM method. The participants from information technology (IT) organizations provided the concepts to describe the target phenomenon of Job Satisfaction; they also identified the associations between the concepts. The researchers used coding rules to aggregate similar concepts to produce a composite RCM. The researchers proposed potential evidence measures that could be used to evaluate the model. This chapter discusses the steps necessary to transform a causal map into an evidential diagram. The evidential diagram can then be analyzed using belief functions technique with survey data, thereby extending the research from a discovery and explanation stage to testing and prediction. An example is provided to demonstrate these steps. This chapter also provides the basics of Dempster-Shafer theory of belief functions and a step-by-step description of the propagation process of beliefs in tree like evidential diagrams. 2 Belief Function Approach to Evidential Reasoning in Causal Maps