  To design trustworthy Bayesian studies, criteria for posterior-based
operating characteristics - such as power and the type I error rate - are often
defined in clinical, industrial, and corporate settings. These posterior-based
operating characteristics are typically assessed by exploring sampling
distributions of posterior probabilities via simulation. In this paper, we
propose a scalable method to determine optimal sample sizes and decision
criteria that maps posterior probabilities to low-dimensional conduits for the
data. Our method leverages this mapping and large-sample theory to explore
sampling distributions of posterior probabilities in a targeted manner. This
targeted exploration approach prompts consistent sample size recommendations
with fewer simulation repetitions than standard methods. We repurpose the
posterior probabilities computed in that approach to efficiently investigate
various sample sizes and decision criteria using contour plots.
