Bayesian Discovery Sampling: A Simple Model of Bayesian Inference in Auditing

Once auditors have been convinced of the advantages of Bayesian inference, they do not have the same difficulties in practical applications as statisticians. The mathematical formulations of prior and posterior probabilities need only to correspond with the auditor's subjective ideas about the presence of errors in a population to be audited; exact derivations are left to the specialists. The auditor, however, has other problems to solve: (1) How can he objectively specify his prior knowledge about the population? (2) How can he objectively interpret posterior probabilities so that he can decide how to audit this population? In this paper these questions are answered by showing that the methodology of discovery sampling gives all the information needed to specify the prior and to interpret the posterior densities. This results in a Bayesian version of a methodology that has been used by auditors for a number of years. Using the Bayesian model of discovery sampling presented in this paper, auditors will not only be able to reduce sample sizes but will also know the exact importance of the assumptions they have made in order to achieve this efficiency.