The Belief-Function Approach to Aggregating Audit Evidence

This is the peer reviewed version of the following article: Srivastava, R. P., "The Belief-Function Approach to Aggregating Audit Evidence" International Journal of Intelligent Systems, Vol. 10, No. 3, March 1995, pp. 329-356., which has been published in final form at http://doi.org/10.1002/int.4550100304. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.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

Theoretical investigation of energy-trapping mechanism by atomic systems

© 1978 The American Physical SocietyThe theoretical results are presented here in detail for the atomic device proposed earlier by the author. This device absorbs energy from a continuous radiation source and stores some of it with atoms in metastable states for a long time without any loss. At a later time, when the energy is required, the system can be "triggered" by an external perturbing field to release the energy in the form of a strong pulse of radiation

Alternative Form of Dempster's Rule for Binary Variables

This is the author's final draft. The publisher's official version is available electronically from: .This article develops an alternative form of Dempster’s rule of combination for binary variables. This alternative form does not only provide a closed form formulae for efficient computation but also enables researchers to develop closed form analytical formulae for assessing risks such as information security risk, fraud risk, audit risk, independence risk, etc., involved in assurance services. We demonstrate the usefulness of the alternative form in calculating the overall information security risk and also in developing an analytical model for assessing fraud risk

Decision Making Under Ambiguity: A Belief-function Perspective

This is the publisher's version, which is being shared with permission, and which is also available electronically from: http://acs.polsl.pl/In this article, we discuss problems with probability theory in representing uncertainties encountered in the "real world" and show how belief functions can overcome these difficulties. Also, we discuss an expected utility approach of decision making under ambiguity using the belief function framework. In particular, we develop a proposition for decision making under ambiguity using the expected utility theory. This proposition is based on Strat's approach of resolving ambiguity in the problem using belief functions. We use the proposition to explain the Ellsberg paradox and model the decision making behavior under ambiguity. We use the empirical data of Einhorn and Hogarth to validate the proposition. Also, we use the proposition to predict several decision making behaviors under ambiguity for special conditions. Furthermore, we discuss the general condition under which the "switching" behavior, as observed by Einhorn and Hogarth, will occur using the concept of "precision measure" in the expected utility theory

The Belief-Function Approach to Aggregating Audit Evidence

This is the author's final draft. The publisher's official version is available from: 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

An Introduction to Evidential Reasoning for Decision Making under Uncertainty: Bayesian and Belief Functions Perspectives

The main purpose of this article is to introduce the evidential reasoning approach, a research methodology, for decision making under uncertainty. Bayesian framework and Dempster-Shafer theory of belief functions are used to model uncertainties in the decision problem. We first introduce the basics of the DS theory and then discuss the evidential reasoning approach and related concepts. Next, we demonstrate how specific decision models can be developed from the basic evidential diagrams under the two frameworks. It is interesting to note that it is quite efficient to develop Bayesian models of the decision problems using the evidential reasoning approach compared to using the ladder diagram approach as used in the auditing literature. In addition, we compare the decision models developed in this paper with similar models developed in the literature

Application of Uncertain Reasoning to Business Decisions: An Introduction

This is the author's final draft. The publisher's official version is available from: http://www.som.buffalo.edu/isinterface/ISFrontiers

Applications of Belief Functions in Business Decisions: A Review

This is the author's final draft. The publisher's official version is available from: .In this paper, we review recent applications of Dempster-Shafer theory (DST) of belief functions to auditing and business decision-making. We show how DST can better map uncertainties in the application domains than Bayesian theory of probabilities. We review the applications in auditing around three practical problems that challenge the effective application of DST, namely, hierarchical evidence, versatile evidence, and statistical evidence. We review the applications in other business decisions in two loose categories: judgment under ambiguity and business model combination. Finally, we show how the theory of linear belief functions, a new extension of DST, can provide an alternative solution to a wide range of business problems

Structural Analysis of Audit Evidence Using Belief Functions

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

Assurance on XBRL Instance Document: A Conceptual Framework of Assertions

XBRL stands for extensible business reporting language. It is an XML based computer language for reporting business information. In December 2008, the United States Securities and Exchange Commission (US SEC) voted to require public filers to provide a supplemental exhibit of their financial statements (including footnotes) in XBRL, with the top approximately 500 public companies required to comply with this new requirement starting on June 15, 2009, and the phase-in of this requirement for the other filers to be completed on June 15, 2011. The file created using the XRBL language is called an XBRL instance document. Under this requirement, the filers are not required to obtain a third party assurance on the XBRL instance document. The main reason for not requiring a third party independent assurance of XBRL instance documents is to encourage filers to comply with the SEC requirement without incurring much added costs. In addition, to encourage the filers to comply with this requirement, the SEC is not holding filers legally liable of any errors in the filed XBRL instance documents so long as they look similar to the standard reports when viewed using the SEC viewer. Even though the SEC is not currently requiring a third party assurance of the XBRL instance documents of the SEC filings, it is in the best interest of the public that these documents be assured. Although there have been efforts by both the practitioners and academics to investigate issues involved in providing assurance on XBRL documents, these efforts have been focused on the specifics of the assurance process and the difficulties involved in it, and not on developing a framework of assertions. Even the American Institute of Certified Public Accountants recent publication SOP 09-1 provides only an illustrative list of management assertions for handling the XBRL-tagging engagements under the SSAEs as agreed-upon procedures without considering a framework. Without a conceptual framework, the assurance process for XBRL instance document would be ad hoc and inconsistent. This paper develops a set of assertions for providing assurance on XBRL instance documents similar to the management assertions for financial audits. Further, we discuss how such a framework would assist auditors in planning and evaluating such an engagement by collecting appropriate items of evidence pertaining to specific assertions to form an opinion whether the instance document is a true representation of the standard format (i.e., ASCII or HTML) document. We also discuss how the use of new technology would make the assurance process more effective and efficient