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 leverages 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.

翻译：为了设计可信的贝叶斯研究，在临床、工业和企业环境中，通常需要定义基于后验的运营特征（如统计功效和第I类错误率）的准则。这些基于后验的运营特征通常通过模拟探索后验概率的抽样分布来评估。本文提出一种可扩展方法以确定最优样本量和决策准则，该方法利用大样本理论有针对性地探索后验概率的抽样分布。这种定向探索方法能够比标准方法用更少的模拟重复次数得出一致的样本量推荐。我们重新利用该方法中计算的后验概率，通过等高线图高效地研究不同样本量和决策准则。