Abstract

There has been strong recent interest in testing interval null hypotheses for improved scientific inference. For example, Lakens et al. and Lakens and Harms use this approach to study if there is a prespecified meaningful treatment effect in gerontology and clinical trials, instead of a point null hypothesis of any effect. Two popular Bayesian approaches are available for interval null hypothesis testing. One is the standard Bayes factor and the other is the region of practical equivalence (ROPE) procedure championed by Kruschke and others over many years. This article connects key quantities in the two approaches, which in turn allow us to contrast two major differences between the approaches with substantial practical implications. The first is that the Bayes factor depends heavily on the prior specification while a modified ROPE procedure is very robust. The second difference is concerned with the statistical property when data are generated under a neutral parameter value on the common boundary of competing hypotheses. In this case, the Bayes factors can be severely biased whereas the modified ROPE approach gives a reasonable result. Finally, the connection leads to a simple and effective algorithm for computing Bayes factors using draws from posterior distributions generated by standard Bayesian programs such as BUGS, JAGS, and Stan.

摘要

最近人们对测试区间零假设以改进科学推理产生了浓厚的兴趣。例如，Lakens 等人。Lakens 和 Harms 使用这种方法来研究在老年学和临床试验中是否存在预先指定的有意义的治疗效果，而不是任何效果的零点假设。两种流行的贝叶斯方法可用于区间原假设检验。一个是标准贝叶斯因子，另一个是 Kruschke 等人多年来倡导的实际等效区域 (ROPE) 过程。本文将两种方法中的关键量联系起来，这反过来又使我们能够对比具有实质性实际意义的方法之间的两个主要差异。第一个是贝叶斯因子在很大程度上取决于先前的规范，而修改后的 ROPE 程序非常稳健。第二个区别与在竞争假设的公共边界上的中性参数值下生成数据时的统计特性有关。在这种情况下，贝叶斯因子可能存在严重偏差，而修改后的 ROPE 方法给出了合理的结果。最后，这种联系导致了一种简单而有效的算法，该算法使用从标准贝叶斯程序（如 BUGS、JAGS 和 Stan）生成的后验分布中抽取来计算贝叶斯因子。贝叶斯因子可能存在严重偏差，而修改后的 ROPE 方法给出了合理的结果。最后，这种联系导致了一种简单而有效的算法，该算法使用从标准贝叶斯程序（如 BUGS、JAGS 和 Stan）生成的后验分布中抽取来计算贝叶斯因子。贝叶斯因子可能存在严重偏差，而修改后的 ROPE 方法给出了合理的结果。最后，这种联系导致了一种简单而有效的算法，该算法使用从标准贝叶斯程序（如 BUGS、JAGS 和 Stan）生成的后验分布中抽取来计算贝叶斯因子。