On a Bayesian sample size determination problem with applications to auditing

The problem motivating this article is the determination of sample size at the substantive testing stage of a financial audit. An error in an audit account is said to occur when there is a non-zero difference between its book value and true value. A typical financial auditing task involves several stages and usually a large number of potential items are available for testing at each stage. The sample size determination problem is to find an optimum fixed number of items which must be tested so that the quantitative risk of a wrong decision is bounded by a pre-specified quantity. Senior auditors often have strong subjective opinions regarding the state of the accounts being audited which naturally leads to the choice of Bayesian methods. Solutions are proposed under various model assumptions. A combination of analytical and simulation based techniques is proposed and some theoretical results are obtained. The methods developed, however, are quite general and can be applied to other sample size determination (SSD) problems. A number of numerical illustrations are given