Bayesian Adaptations of Four Popular Audit Sampling Estimators

Testing a financial population for material misstatement is a standard audit activity. However, this can be challenging when the population contains many errors or when both over- and understatements occur. In such situations, auditors typically rely on four popular frequentist methods: the direct, difference, ratio, and regression estimators. Although widely applied, these methods suffer from a fundamental limitation: they cannot provide direct evidential support for the auditor’s conclusion about the population misstatement. Bayesian approaches can provide this evidential support, but corresponding adaptations of these estimators are largely absent in the literature. This article addresses that gap in three ways. First, it develops a unified Bayesian posterior predictive framework for all four estimators that enables both estimation and hypothesis testing. Second, it proposes a default prior for computing Bayes factors that is suitable for routine audit applications. Third, it provides an open-source software implementation to facilitate practical adoption of these methods.