  Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or
credible intervals to inform data-driven decision making. We propose a
framework for power curve approximation with such hypothesis tests. We present
a fast approach to explore the approximate sampling distribution of posterior
probabilities when the conditions for the Bernstein-von Mises theorem are
satisfied. We extend that approach to consider segments of such sampling
distributions in a targeted manner for each sample size explored. These
sampling distribution segments are used to construct power curves for various
types of posterior analyses. Our resulting method for power curve approximation
is orders of magnitude faster than conventional power curve estimation for
Bayesian hypothesis tests. We also prove the consistency of the corresponding
power estimates and sample size recommendations under certain conditions.
