Department of Statistics, Texas A&M University, College Station, TX 77843-3143.
Proc Natl Acad Sci U S A. 2023 Feb 21;120(8):e2217331120. doi: 10.1073/pnas.2217331120. Epub 2023 Feb 13.
Bayes factors represent a useful alternative to -values for reporting outcomes of hypothesis tests by providing direct measures of the relative support that data provide to competing hypotheses. Unfortunately, the competing hypotheses have to be specified, and the calculation of Bayes factors in high-dimensional settings can be difficult. To address these problems, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs depend on a single noncentrality parameter that can be expressed as a function of standardized effects, and plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies. Such summaries eliminate the need for arbitrary -value thresholds to define "statistical significance." Because BFFs are defined using nonlocal alternative prior densities, they provide more rapid accumulation of evidence in favor of true null hypotheses without sacrificing efficiency in supporting true alternative hypotheses. BFFs can be expressed in closed form and can be computed easily from , , , and statistics.
贝叶斯因子为报告假设检验结果提供了一种有用的替代方法，与 P 值相比，它可以直接衡量数据对竞争假设的相对支持程度。不幸的是，需要指定竞争假设，并且在高维环境中计算贝叶斯因子可能很困难。为了解决这些问题，我们直接从常见的检验统计量定义贝叶斯因子函数（BFF）。BFF 取决于一个单一的非中心参数，该参数可以表示为标准化效应的函数，并且 BFF 与效应量的关系图提供了假设检验的信息性总结，这些总结可以很容易地在研究之间进行汇总。这种总结消除了使用任意 P 值阈值来定义“统计显著性”的需要。由于 BFF 是使用非局部替代先验密度定义的，因此它们可以在不牺牲支持真实替代假设效率的情况下，更快速地积累有利于真实零假设的证据。BFF 可以用封闭形式表示，并且可以很容易地从 t、F、 和 统计量中计算出来。
