ABSTRACT Many Bayes factors have been proposed for comparing population means in two-sample (independent samples) studies. Recently, Wang and Liu presented an “objective” Bayes factor (BF) as an alternative to a “subjective” one presented by Gönen et al. Their report was evidently intended to show the superiority of their BF based on “undesirable behavior” of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to “lay all cards on the table.” What distinguishes the various BFs in the two-sample problem is the choice of priors (cards) for the model parameters. This article discusses desiderata of BFs that have been proposed, and proposes a new criterion to compare BFs, no matter whether subjectively or objectively determined. A BF may be preferred if it correctly classifies the data as coming from the correct model most often. The criterion is based on a famous result in classification theory to minimize the total probability of misclassification. This criterion is objective, easily verified by simulation, shows clearly the effects (positive or negative) of assuming particular priors, provides new insights into the appropriateness of BFs in general, and provides a new answer to the question, “Which BF is best?”

中文翻译：

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比较两个样本比较的客观和主观贝叶斯因素：分类定理的实际应用

摘要 人们提出了许多贝叶斯因子来比较两个样本（独立样本）研究中的总体平均值。最近，Wang 和 Liu 提出了一种“客观”贝叶斯因子 (BF)，作为 Gönen 等人提出的“主观”贝叶斯因子的替代方案。他们的报告显然是为了基于 BF 的“不良行为”来展示 BF 的优越性。贝叶斯模型的一个美妙之处在于它们提供了“将所有牌摆在桌面上”的机会。双样本问题中各种 BF 的区别在于模型参数的先验（卡片）的选择。本文讨论了已提出的 BF 的必要条件，并提出了一种新的标准来比较 BF，无论是主观还是客观确定。如果 BF 将数据正确分类为最常来自正确的模型，则 BF 可能是首选。该标准基于分类理论中的一个著名结果，旨在最大限度地减少错误分类的总概率。该标准是客观的，易于通过模拟验证，清楚地显示了假设特定先验的影响（正面或负面），为一般 BF 的适当性提供了新的见解，并为“哪种 BF 最好？”这一问题提供了新的答案。 ”