Bayesian sequential inference for error rates and error amounts in accounting data

In the literature about estimating error rates and error amounts in accounting data, a number of observations stand out: (1) The error rates are usually very low, which render many existing statistical procedures inappropriate for estimating and hypothesis testing of error rates and error amounts. (2) The auditors and/or accountants often have a lot of prior information about the data that they would like to incorporate in the estimation process. This renders Bayesian methods attractive to them. (3) Sequential methods would seem appropriate for some of these problems, yet there is a noticeable lack of such methods in the relevant literature. (4) The error amounts in these populations follow nonstandard distributions. In this paper we propose Bayesian sequential inference procedures for error rates and error amounts in accounting data that may be useful in improving the situation. Because computational difficulties arise in evaluating exact densities, normal and beta approximations are given for univariate inference. For joint inference on the error rate and the error amount the exact density is described and a Dirichlet approximation is proposed.