In one-sided testing, Bayesians and frequentists differ on whether or not there is discrepancy between the inference based on the posterior model probability and that based on the p value. We add some arguments to this debate analyzing the discrepancy for moderate and large sample sizes. For small and moderate samples sizes, the discrepancy is measured by the probability of disagreement. Examples of the discrepancy on some basic sampling models indicate the somewhat unexpected result that the probability of disagreement is larger when sampling from models in the alternative hypothesis that are not located at the boundary of the hypotheses. For large sample sizes, we prove that the Bayesian one-sided testing is, under mild conditions, consistent, a property that is not shared by the frequentist procedure. Further, the rate of convergence is \(O(e^{nA})\), where A is a constant that depends on the model from which we are sampling. Consistency is also proved for an extension to multiple hypotheses.

在片面检验中，贝叶斯学派和频率学派的分歧在于基于后验模型概率的推理与基于p的推理之间是否存在差异。价值。我们为这场辩论增加了一些论据，分析了中等和大样本量的差异。对于小样本和中等样本量，差异是通过不一致的概率来衡量的。一些基本抽样模型的差异示例表明，当从不位于假设边界的替代假设中的模型中抽样时，出现不一致的概率更大的有点出乎意料的结果。对于大样本量，我们证明贝叶斯单边测试在温和条件下是一致的，这是频率论程序不共享的属性。此外，收敛速度为\(O(e^{nA})\)，其中A是一个常数，取决于我们从中采样的模型。对于多个假设的扩展也证明了一致性。