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 defines a distribution for the sample size that controls the length of posterior highest density intervals, where targets for the interval length are calibrated to yield desired power for the equivalence test. We prove the normality of the limiting distribution for the sample size and introduce a two-stage approach for estimating this distribution in the nonlimiting case. This approach is much faster than traditional power calculations for Bayesian equivalence tests, and it requires users to make fewer choices than traditional simulation-based methods for Bayesian sample size determination.

翻译：等价检验可以得出两个特征实际上等价的结论。我们提出了一种通过后验概率快速确定贝叶斯等价检验样本量的框架。假设数据是由固定参数的统计模型生成的，以便进行样本量确定。我们的框架定义了控制后验最高密度区间长度的样本量分布，并通过校准区间长度的目标来获得等价检验所需的功效。我们证明了样本量极限分布的正态性，并引入了一种两阶段方法来估计非极限情况下的该分布。该方法比传统的贝叶斯等价检验功效计算快得多，并且相比传统的基于模拟的贝叶斯样本量确定方法，用户需要选择的参数更少。