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.

翻译：为设计可信的贝叶斯研究，临床、工业和商业环境中常需定义基于后验的运作特性标准（如统计功效和第一类错误率）。这类后验运作特性通常通过模拟探索后验概率的抽样分布进行评估。本文提出一种可扩展方法，用于确定最优样本量和决策准则——该方法将后验概率映射至数据的低维通道。我们利用这种映射与大样本理论，以定向方式探索后验概率的抽样分布。相较于传统方法，这种定向探索策略能以更少的模拟重复次数给出一致的样本量建议。通过重用该方法中计算出的后验概率，可借助等高线图高效研究不同样本量及决策准则。