Belief-Function Formulas for Audit Risk

Abstract

BELIEF-FUNCTION FORMULAS FOR AUDIT RISK SYNOPSIS AND INTRODUCTION: This article relates belief functions to the structure of audit risk and provides formulas for audit risk under certain simplifying assumptions. These formulas give plausibilities of error in the belief-function sense. We believe that belief-function plausibility represents auditors' intuitive understanding of audit risk better than ordinary probability. The plausibility of a statement, within belief-function theory, measures the extent to which we lack evidence against the statement. High plausibility for error indicates only a lack of assurance, not positive evidence that there is error. Before collecting, analyzing, and aggregating the evidence, an auditor may lack any assurance that a financial statement is correct, and in this case will attribute very high plausibility to material misstatement. This high plausibility does not necessarily indicate any evidence that the statement is materially misstated, and hence it is inappropriate to interpret it as a probability of material misstatement. The SAS No. 47 formula for audit risk is based on a very simple structure for audit evidence. The formulas we derive in this article are based on a slightly more complex but still simplified structure, together with other simplifying assumptions. We assume a tree-type structure for the evidence, assume that all evidence is affirmative and that each variable in the tree is binary. All these assumptions can be relaxed. As they are relaxed, however, the formulas become more complex and less informative, and it then becomes more useful to think in terms of computer algorithms rather than in terms of formulas (Shafer et al. 1988). In general, the structure of audit evidence corresponds to a network of variables. We derive formulas only for the case in which each item of evidence bears either on all the audit objectives of an account or on all the accounts in the financial statement, as in figure 1, so that the network is a tree. Usually, however, there will be some evidence that bears on some but not all objectives for an account, on some but not all accounts, or on objectives at different levels; in this case, the network will not be a tree.

The belief-function approach to aggregating audit evidence

“…As discussed by Shafer and Srivastava (1992), plausibility in '~ar' is equivalent to the audit risk. Thus, we have 0.04693 risk that the account is materially misstated.…”

“…Shafer and Srivastava (1990) contend that uncertainty in the audit evidence cannot be fully described in terms of probability; the belief-function theory provides a better framework. Recently, Srivastava and Shafer (1992) have discussed the problems with interpreting audit risk as probabilities and have provided a belief-function interpretation of the risk that makes intuitive sense. They have also derived belief-function formulas for audit risk.…”

Checklist-Based Risk Analysis with Evidential Reasoning

“…In this article, the overall structure for measuring risk with uncertainty follows the structure of Srivastava's belief function formula Shafer 1992, Srivastava andMock 2000). He has developed a special network diagram to apply belief functions to various applications in the accounting domain such as the calculation of audit risk (Srivastava and Shafer 1992) and the WebTrust assurance service (Srivastava and Mock 2000).…”

“…He has developed a special network diagram to apply belief functions to various applications in the accounting domain such as the calculation of audit risk (Srivastava and Shafer 1992) and the WebTrust assurance service (Srivastava and Mock 2000). His model starts from building a network diagram called an evidential network.…”

“…The subscript represents the name of variable to which evidence is applied ('A' stands for the asset variable in this case). The ¹ A major part of this section is based on Srivastava and Shafer (1992). m element 'a' represents, for example, the proposition that 'asset i is secure' and the element '¬ a' represents the proposition that 'asset i is NOT secure'.…”