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 CC-BY Attribution 4.0 International license and is available at https://psyarxiv.com/5p2qt/. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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HDI + ROPE 决策规则在逻辑上不连贯，但我们可以修复它。


贝叶斯最高密度区间加上实际等价区域 (HDI + ROPE) 决策规则是一种越来越常见的测试空参数值的方法。决策过程涉及后验最高密度区间 (HDI) 与预先指定的实际等效区域之间的比较。然后根据这些间隔之间的重叠（或缺乏）来接受或拒绝空参数值。在这里，我们从理论上和通过例子证明这个过程在逻辑上是不连贯的。由于 HDI 不是变换不变的，因此最终的推理决策取决于统计模型的统计任意性和科学上不相关的属性。这种不连贯性源于概率密度和概率本身之间的常见混淆。 HDI + ROPE 过程依赖于表征后验密度，而不是直接基于概率。最后，我们提出了替代贝叶斯测试程序的建议，这些测试程序不表现出这种病态，并以分位数间隔的形式提供“快速修复”。本文是作者的作品，根据原文重新格式化，该文章在 CC-BY Attribution 4.0 International 许可下发布，可在 https://psyarxiv.com/5p2qt/ 上获取。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。