张量标量比$r$和中微子质量$m_ν$的贝叶斯证据：均匀先验与对数先验的影响
Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_ν$: Effects of uniform vs logarithmic priors
摘要：
我们审查的效果，选择一个统一的或对数先验的贝叶斯证据，因此对贝叶斯模型的比较时，数据只提供一个单侧约束的参数。利用普朗克2018年的宇宙微波背景温度和偏振数据以及中微子振荡实验的NuFIT 5.0数据，我们研究了两个特殊的例子：原始扰动的张量标量比$r$和单个中微子$m_ν$的质量。我们认为，Kullback-Leibler分歧，也称为相对熵，数学量化的奥卡姆罚。我们进一步展示了贝叶斯证据如何在改变上约束参数的先验下界时保持不变。虽然张量-标量比的均匀先验不利于$r$ -扩展，但与基本LCDM模型相比，其几率约为1：20，切换到对数先验使两个模型基本上具有相同的可能性。在最轻中微子质量的均匀先验的情况下，具有单个大质量中微子的LCDM比具有可变中微子质量的扩展更受欢迎，几率为20：1，对数先验的几率约为2：1。对于前面的两个选项，我们只得到一个非常轻微的偏好正常的倒中微子层次与贝叶斯赔率约3：2最多。
英文摘要：
We review the effect that the choice of a uniform or logarithmic prior has on the Bayesian evidence and hence on Bayesian model comparisons when data provide only a one-sided bound on a parameter. We investigate two particular examples: the tensor-to-scalar ratio $r$ of primordial perturbations and the mass of individual neutrinos $m_ν$, using the cosmic microwave background temperature and polarisation data from Planck 2018 and the NuFIT 5.0 data from neutrino oscillation experiments. We argue that the Kullback-Leibler divergence, also called the relative entropy, mathematically quantifies the Occam penalty. We further show how the Bayesian evidence stays invariant upon changing the lower prior bound of an upper constrained parameter. While a uniform prior on the tensor-to-scalar ratio disfavours the $r$-extension compared to the base LCDM model with odds of about 1:20, switching to a logarithmic prior renders both models essentially equally likely. LCDM with a single massive neutrino is favoured over an extension with variable neutrino masses with odds of 20:1 in case of a uniform prior on the lightest neutrino mass, which decreases to roughly 2:1 for a logarithmic prior. For both prior options we get only a very slight preference for the normal over the inverted neutrino hierarchy with Bayesian odds of about 3:2 at most.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
