Etz Alexander, Chávez de la Peña Adriana F, Baroja Luis, Medriano Kathleen, Vandekerckhove Joachim
Department of Psychology, University of Texas at Austin.
Department of Cognitive Sciences, University of California, Irvine.
Psychol Methods. 2024 May 23. doi: 10.1037/met0000660.
The Bayesian highest-density interval plus region of practical equivalence (HDI + ROPE) decision rule is an increasingly common approach to testing null parameter values. The decision procedure involves a comparison between a posterior highest-density interval (HDI) and a prespecified region of practical equivalence. One then accepts or rejects the null parameter value depending on the overlap (or lack thereof) between these intervals. Here, we demonstrate, both theoretically and through examples, that this procedure is logically incoherent. Because the HDI is not transformation invariant, the ultimate inferential decision depends on statistically arbitrary and scientifically irrelevant properties of the statistical model. The incoherence arises from a common confusion between probability density and probability proper. The HDI + ROPE procedure relies on characterizing posterior densities as opposed to being based directly on probability. We conclude with recommendations for alternative Bayesian testing procedures that do not exhibit this pathology and provide a "quick fix" in the form of quantile intervals. This article is the work of the authors and is reformatted from the original, which was published under a license and is available at https://psyarxiv.com/5p2qt/. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
贝叶斯最高密度区间加实际等效区域（HDI + ROPE）决策规则是检验零假设参数值时越来越常用的方法。该决策程序涉及比较后验最高密度区间（HDI）和预先指定的实际等效区域。然后，根据这些区间之间的重叠情况（或没有重叠）来接受或拒绝零假设参数值。在此，我们通过理论和实例证明，该程序在逻辑上是不一致的。由于HDI不是变换不变的，最终的推断决策取决于统计模型中在统计上任意且与科学无关的属性。这种不一致源于概率密度和概率本身之间常见的混淆。HDI + ROPE程序依赖于对后验密度进行特征描述，而不是直接基于概率。我们最后给出了关于替代贝叶斯检验程序的建议，这些程序不会出现这种问题，并以分位数区间的形式提供了一种“快速修复”方法。本文是作者的作品，是对原文的重新排版，原文根据许可发布，可在https://psyarxiv.com/5p2qt/获取。（PsycInfo数据库记录（c）2024美国心理学会，保留所有权利）
