A note on the Quasi-Bayesian audit risk model for dollar unit sampling1

The Quasi-Bayesian (QB) model generates a complete probability mass function on the total amount of error in an accounting population for any random sample of dollar units or physical units. This probability mass function is used to estimate upper bounds (UBs) on the total amount of error in an accounting population. The underlying QB formulation can be summarized as Bayes' Theorem with a maximum likelihood, calculated using the multinomial distribution, substituted for the unknown likelihood. Any prior can be used. McCray did not provide any theoretical justification for using a maximum likelihood. To date the justification for the QB estimated UBs rests on intuitive arguments limited simulations and 'windtunnel' tests. All these suggest the QB UBs may be reliable for audit purposes. This paper provides the theoretical justification for using a maximum likelihood in the QB model. It is based on the concept of 'partial prior information'.