The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's scale, used to assess the test, is arbitrary. Moreover, the standard use of Bayes' ratio is often criticized for being unable to reject models. In this paper, we address these shortcoming by promoting evidences and evidence ratios to frequentist statistics and deriving their sampling distributions. By comparing the evidence ratios to their sampling distributions, poor fitting models can now be rejected. Our method additionally does not depend on the prior in the limit of very weak priors, thereby safeguarding the experimenter against premature rejection of a theory with a uninformative prior, and replaces the arbitrary Jeffrey's scale by probability thresholds for rejection. We provide analytical solutions for some simplified cases (Gaussian data, linear parameters, and nested models), and we apply the method to cosmological supernovae Ia data. We dub our method the FB method, for Frequentist-Bayesian.

翻译：贝叶斯证据比是宇宙学中常用的一种模型比较工具。然而，该方法存在若干问题：即使在无信息先验的极限情况下，贝叶斯比仍依赖于先验；用于评估检验的杰弗里斯尺度具有任意性。此外，贝叶斯比的标准应用常因无法拒绝模型而受到批评。本文通过将证据及证据比提升为频率统计量并推导其采样分布来弥补这些不足。通过将证据比与其采样分布进行比较，可以拒绝拟合不良的模型。在极弱先验的极限下，我们的方法额外不依赖于先验，从而保护实验者避免因无信息先验而过早否定理论，并用概率阈值替代了任意的杰弗里斯尺度。我们针对若干简化情形（高斯数据、线性参数及嵌套模型）给出了解析解，并将该方法应用于宇宙学Ia型超新星数据。我们将此方法称为FB方法，即频率-贝叶斯混合方法。