Representation of Interrelationships among Binary Variables under Dempster-Shafer Theory of Belief Functions

This is the peer reviewed version of the following article: Srivastava, R. P., L. Gao, and P. Gillett. " Representation of Interrelationships among Binary Variables under Dempster-Shafer Theory of Belief Functions" (pre-publication version), 2009, International Journal of Intelligent Systems, Volume 24 Issue 4, pp. 459 - 475, which has been published in final form at http://doi.org/10.1002/int.20347. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.This paper presents an algorithm for developing models under Dempster-Shafer theory of belief functions for categorical and 'uncertain' logical relationships among binary variables. We illustrate the use of the algorithm by developing belief-function representations of the following categorical relationships: 'AND', 'OR', 'Exclusive OR (EOR)' and 'Not Exclusive OR (NEOR)', and 'AND-NEOR' and of the following uncertain relationships: 'Discounted AND', 'Conditional OR', and 'Weighted Average'. Such representations are needed to fully model and analyze a problem with a network of interrelated variables under Dempster-Shafer theory of belief functions. In addition, we compare our belief-function representation of the 'Weighted Average' relationship with the 'Weighted Average' representation developed and used by Shenoy and Shenoy8. We find that Shenoy and Shenoy representation of the weighted average relationship is an approximation and yields significantly different values under certain conditions

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

An Information Systems Security Risk Assessment Model Under Dempster- Schafer Theory of Belief Functions

This is the author's final draft. The publisher's official version is available from:.This study develops an alternative methodology for the risk analysis of information systems security (ISS), an evidential reasoning approach under the Dempster-Shafer theory of belief functions. The approach has the following important dimensions. First, the evidential reasoning approach provides a rigorous, structured manner to incorporate relevant ISS risk factors, related counter measures and their interrelationships when estimating ISS risk. Secondly, the methodology employs the belief function definition of risk, that is, ISS risk is the plausibility of information system security failures. The proposed approach has other appealing features, such as facilitating cost-benefit analyses to help promote efficient ISS risk management. The paper both elaborates the theoretical concepts and provides operational guidance for implementing the method. The method is illustrated using a hypothetical example from the perspective of management and a real-world example from the perspective of external assurance providers. Sensitivity analyses are performed to evaluate the impact of important parameters on the model’s results

An Evidential Reasoning Approach to Sarbanes-Oxley Mandated Internal Control Risk Assessment

This is the peer reviewed version of the following article: Mock, T., L. Sun, R. P. Srivastava, and M. Vasarhelyi. " An Evidential Reasoning Approach to Sarbanes-Oxley Mandated Internal Control Risk Assessment under Dempster-Shafer Theory", 2009, ABACUS, Vol. 45, No. 1, pp. 66-87. , which has been published in final form at http://doi.org/10.1016/j.accinf.2008.10.003. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In response to the enactment of the Sarbanes-Oxley Act 2002 and of the release of the Public Company Accounting Oversight Board (PCAOB) Auditing Standard No. 5, this study develops a risk-based evidential reasoning approach for assessing the effectiveness of internal controls over financial reporting (ICoFR). This approach provides a structured methodology for assessing the effectiveness of ICoFR by considering relevant factors and their interrelationships. The Dempster-Shafer theory of belief functions is utilized for representing risk. First, we develop a generic ICoFR assessment model based upon a Big 4 audit firm’s approach and apply it to a real-world example. Then, based on this model, we develop a quantitative representation of various levels of ICoFR effectiveness and related risk-assessment as defined by the PCAOB and contrast these representations with levels implied by Auditing Standard No. 5. In doing so, we demonstrate the potential value of formal risk assessment models in both facilitating the assessment of risks in an individual engagement and in assessing the effects of different regulations

Bayesian and Belief-Functions Formulas for Auditor Independence Risk Assessment

This is the authors final draft. The publisher's official version is available electronically from: .This paper illustrates two formulas for assessing independence risk based on the Bayesian and belief-functions frameworks. These formulas can be used to assess the role of threats to auditor independence as well as the role of threat-mitigating safeguards. Also, these formulas provide a basis for evaluation of an audit firm’s independence risk and a framework to educate stakeholders about the threats faced by the audit firm and the role of effective safeguards in mitigating these risks. The formulas also provide a means for regulators and lawmakers to evaluate whether they have effective safeguards in place given the existence of threats and for auditors to signal to various stakeholders that they have identified significant threats and have effective safeguards in place. To show the potential usefulness of these analytical models, several illustrations addressing increased transparency and the potential impact of regulations are presented

An Evidential Reasoning Approach to Fraud Risk Assessment under Dempster-Shafer Theory: A General Framework

This paper develops a general framework under Dempster-Shafer theory for assessing fraud risk in a financial statement audit by integrating the evidence pertaining to the presence of fraud triangle factors (incentives, attitude and opportunities), and evidence concerning both account-based and evidence-based fraud schemes. This framework extends fraud risk assessment models in prior research in three respects. 1) It integrates fraud schemes, both account schemes through which accounts are manipulated, and evidence schemes through which frauds are concealed, into a single framework. 2) It incorporates prior fraud frequency information obtained from the Accounting and Auditing Enforcement Releases issued by the Securities and Exchange Commission into an evidential network which uses Conditional OR relationships among assertions. 3) The framework provides a structured approach for connecting risk assessment, audit planning, and evaluation of audit results. The paper uses a real fraud case to illustrate the application of the framework

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

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