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：贝叶斯证据比值是宇宙学中比较不同模型的常用工具。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，贝叶斯比值仍依赖于先验分布，且用于评估检验的杰弗里斯尺度具有任意性。此外，贝叶斯比值的标准用法常因无法拒绝模型而受到批评。本文通过将证据与证据比值提升为频率学派统计量并推导其抽样分布，以解决这些缺陷。通过将证据比值与其抽样分布进行比较，现在可以拒绝拟合效果差的模型。我们的方法在极弱先验极限下不依赖于先验分布，从而防止实验者因使用无信息先验而过早拒绝理论，并用概率拒绝阈值取代了任意的杰弗里斯尺度。我们为某些简化情形（高斯数据、线性参数和嵌套模型）提供了解析解，并将该方法应用于宇宙学Ia型超新星数据。我们将此方法命名为FB方法（频率学派-贝叶斯方法）。