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.

翻译：贝叶斯假设检验利用后验概率、贝叶斯因子或可信区间来支持数据驱动的决策。我们提出了一个针对此类假设检验的功效曲线近似框架。当满足伯恩斯坦-冯·米塞斯定理的条件时，我们提出了一种快速方法来探索后验概率的近似抽样分布。我们扩展了该方法，以针对每个研究的样本量，有针对性地考虑此类抽样分布的区段。这些抽样分布区段被用于构建各类后验分析的功效曲线。我们最终的功效曲线近似方法，其速度比传统的贝叶斯假设检验功效曲线估计方法快数个数量级。我们还证明了在特定条件下，相应功效估计与样本量建议的一致性。