Equivalence testing allows one to conclude that two characteristics are practically equivalent. We propose a framework for fast sample size determination with Bayesian equivalence tests facilitated via posterior probabilities. We assume that data are generated using statistical models with fixed parameters for the purposes of sample size determination. Our framework leverages an interval-based approach, which defines a distribution for the sample size to control the length of posterior highest density intervals (HDIs). We prove the normality of the limiting distribution for the sample size, and we consider the relationship between posterior HDI length and the statistical power of Bayesian equivalence tests. We introduce two novel approaches for estimating the distribution for the sample size, both of which are calibrated to align with targets for statistical power. Both approaches are much faster than traditional power calculations for Bayesian equivalence tests. Moreover, our method requires users to make fewer choices than traditional simulation-based methods for Bayesian sample size determination. It is therefore more accessible to users accustomed to frequentist methods.

翻译：等价检验允许人们推断两个特征在实际意义上等价。我们提出一个基于后验概率的贝叶斯等价检验框架，用于快速确定样本量。假设数据由固定参数的统计模型生成以服务于样本量确定目的。我们的框架采用基于区间的方法，通过定义样本量的分布来控制后验最高密度区间（HDI）的长度。我们证明了样本量极限分布的正态性，并考虑了后验HDI长度与贝叶斯等价检验统计功效之间的关系。我们引入两种估计样本量分布的新方法，这两种方法均经过校准以匹配统计功效目标。相比贝叶斯等价检验的传统功效计算，两种方法都显著更快。此外，与基于模拟的传统贝叶斯样本量确定方法相比，我们的方法要求用户做出的选择更少，因此对习惯频率学派方法的用户更具可操作性。