An Economical Approach to Design Posterior Analyses

To design Bayesian studies, criteria for the operating characteristics of posterior analyses—such as power and the Type I error rate—are often assessed by estimating sampling distributions of posterior probabilities via simulation. In this work, we propose an economical method to determine optimal sample sizes and decision for such studies. Using our theoretical results that model posterior probabilities as a function of the sample size, we assess operating characteristics throughout the sample size space given simulations conducted at only two sample sizes. These theoretical results are used to construct bootstrap confidence intervals for the sample sizes and decision criteria that reflect the stochastic nature of simulation-based design. The broad applicability and wide impact of our methodology is illustrated using two clinical examples.

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