Bayesian sample size determination for binomial proportions

Abstract. This paper presents several new results on Bayesian sample size deter-mination for estimating binomial proportions, and provides a comprehensive com-parative overview of the subject. We investigate the binomial sample size problem using generalized versions of the Average Length and Average Coverage Criteria, the Median Length and Median Coverage Criteria, as well as the Worst Outcome Criterion and its modied version. We compare sample sizes derived from highest posterior density and equal-tailed credible intervals. In some cases, we derive, for the rst time, closed form sample size formulae, and where this is not possible, we describe various numerical approaches. These range in complexity from Monte Carlo simulations to more sophisticated curve tting techniques, third order an-alytic approximations, and exact, but more computationally-intensive, methods. We compare the accuracy and eciency of the dierent computational methods for each of the criteria and make recommendations about which methods are preferred. Finally, we consider, again for the rst time, issues surrounding prior robustness on the choice of sample size. Examples are given throughout the text