Some Bayesian methods for two auditing problems

Two problems of interest to auditors are: (i) finding an upper bound for the total amount of overstatement of assets in a set of accounts; and (ii) estimating the amount of sales tax owed on a collection of transactions. For the first problem, the Stringer bound has often been used despite the fact that in many cases it is known to be much too large. Here we will introduce a family of stepwise Bayes models that yields bounds that are closely related to the Stringer bound but are less conservative. Then we will show how this approach can also be used for solving the second problem. This will allow practitioners with modest amounts of prior information to select inference procedures with good frequentist properties.