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Axioms for probability and belieffunction propagation
 Uncertainty in Artificial Intelligence
, 1990
"... 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 ..."
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Cited by 135 (17 self)
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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.
An Information Systems Security Risk Assessment Model under DempsterShafer Theory of Belief Functions
 Journal of Management Information Systems
, 2006
"... 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 Unive ..."
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Cited by 9 (1 self)
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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.
BeliefFunction formulas for audit risk
 The Accounting Review
, 1992
"... Willingham for valuable comments on an earlier version of the article. ..."
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Cited by 6 (4 self)
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Willingham for valuable comments on an earlier version of the article.
Structural Analysis of Audit Evidence using Belief Functions. Fuzzy Sets and Systems
 Fuzzy Sets and Systems
, 2002
"... This article performs two types of analysis using DempsterShafer 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, ..."
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Cited by 5 (2 self)
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This article performs two types of analysis using DempsterShafer 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.
Modeling financial portfolios using belief functions
 Belief Functions in Business Decisions, Physica–Verlag
, 2002
"... The main goal of this paper is to demonstrate how the theory of belief functions ..."
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Cited by 5 (3 self)
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The main goal of this paper is to demonstrate how the theory of belief functions
Integrating Statistical and NonStatistical Audit Evidence in Attribute Sampling Using Belief Functions
, 2000
"... The main purpose of this article is to show how one can integrate statistical evidence from attribute sampling with nonstatistical evidence within the DempsterShafer belief function framework. In particular, the article shows: (1) how to determine the sample size in attribute sampling to obtain a ..."
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Cited by 3 (3 self)
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The main purpose of this article is to show how one can integrate statistical evidence from attribute sampling with nonstatistical evidence within the DempsterShafer 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 nonstatistical 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
Belief Function Approach to Evidential Reasoning in Causal Maps
, 2004
"... The purpose of this chapter is to demonstrate the use of evidential reasoning approach under DempsterShafer (DS) 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 unders ..."
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The purpose of this chapter is to demonstrate the use of evidential reasoning approach under DempsterShafer (DS) 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 DempsterShafer theory of belief functions and a stepbystep description of the propagation process of beliefs in tree like evidential diagrams. 2 Belief Function Approach to Evidential Reasoning in Causal Maps
A Hybrid Approach of Evidence Theory and Rough Sets for ISS Risk Assessment
"... Abstract—In electronic business environment, it is critical for an enterprise to assess information systems security (ISS) risks. In this paper we propose an evidence theory and rough sets based approach to objectively represent uncertainty inherent in the ISS risk assessment. Uncertainty in securit ..."
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Abstract—In electronic business environment, it is critical for an enterprise to assess information systems security (ISS) risks. In this paper we propose an evidence theory and rough sets based approach to objectively represent uncertainty inherent in the ISS risk assessment. Uncertainty in security risk management stems from the incompleteness and vagueness of the conditioning attributes that characterize a risk. In the hybrid approach, evidence theory provides a consistent approach to model experts ’ beliefs and develop an evidential diagram to assess the ISS risk that contains various variables such as the IS assets, the related threats, and the corresponding countermeasures. While rough set theory is ideally suited for dealing with vague and incomplete information. Integrating these two approaches provides a way to deal with the uncertain evidence found in the ISS risk assessment and the uncertainty derived from the conflicts of evidence. In a case study, the effectiveness of the proposed approach is evaluated by comparing it with other methods. Index Terms—information systems security (ISS), evidence theory, rough sets I.
article. Integrating Statistical and NonStatistical Audit Evidence Using
, 1993
"... Belief Functions: A Case of Variable Sampling The main purpose of this article is to show how one can integrate statistical and nonstatistical items of evidence under the belief function framework. First, we use the properties of consonant belief functions to define the belief that the true mean of ..."
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Belief Functions: A Case of Variable Sampling The main purpose of this article is to show how one can integrate statistical and nonstatistical items of evidence under the belief function framework. First, we use the properties of consonant belief functions to define the belief that the true mean of a variable lies in a given interval when a statistical test is performed for the variable. Second, we use the above definition to determine the sample size for a statistical test when a desired level of belief is needed from the sample. Third, we determine the level of belief that the true mean lies in a given interval when a statistical test is performed for the variable with a given sample size. We use an auditing example to illustrate the process.