SAMPLE-SIZE CALCULATIONS FOR BINOMIAL PROPORTIONS VIA HIGHEST POSTERIOR DENSITY INTERVALS

Three different Bayesian approaches to sample size calculations based on highest posterior density (HPD) intervals are discussed and illustrated in the context of a binomial experiment. The preposterior marginal distribution of the data is used to find the sample size needed to attain an expected HPD coverage probability for a given fixed interval length. Alternatively, one can find the sample size required to attain an expected HPD interval length for a fixed coverage. These two criteria can lead to different sample size requirements. In addition to averaging, a worst possible outcome scenario is also considered. The results presented here provide an exact solution to a problem recently addressed in the literature.