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arXiv 2408.07700astro-ph.CO
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宇宙学中的轮廓似然:何时、为何及如何,以 $Λ$CDM、大质量中微子和暗能量为例

Profile Likelihoods in Cosmology: When, Why and How illustrated with $Λ$CDM, Massive Neutrinos and Dark Energy

Laura Herold, Elisa G. M. Ferreira, Lukas Heinrich

AI总结:

本文回顾了宇宙学中的频率派轮廓似然方法,利用 Planck 2018 数据评估其在 $Λ$CDM、大质量中微子和暗能量模型中的有效性,并发布了相关代码。

摘要:

使用轮廓似然的频率派参数推断近期在宇宙学文献中受到了越来越多的关注,因为它能提供与贝叶斯可信区间互补的重要信息。在此,我们对宇宙学中的频率派参数推断进行了教学性回顾,重点关注图形化轮廓似然构造何时能给出有意义的约束,即具有正确覆盖率的置信区间。该构造依赖于大数据集的渐近极限假设,如 Wilks 定理。我们在使用 Planck 2018 Plik_lite 数据的三个宇宙学模型背景下评估了此假设的有效性:尽管我们对 $Λ$CDM 模型的测试表明轮廓似然方法给出了正确的覆盖率,但以中微子质量之和作为自由参数的 $Λ$CDM 似乎与边界附近的高斯分布一致,这促使我们使用边界校正或 Feldman-Cousins 图形化方法;对于以暗能量状态方程 $w_0$ 作为自由参数的 $w_0$CDM,我们发现了假设被违反的迹象。最后,我们比较了这些模型的频率派和贝叶斯约束。我们的结果促使在宇宙学中使用图形化轮廓似然方法时需谨慎。伴随本文,我们发布了轮廓似然代码“pinc”。

英文摘要:

Frequentist parameter inference using profile likelihoods has received increased attention in the cosmology literature recently since it can give important complementary information to Bayesian credible intervals. Here, we give a pedagogical review of frequentist parameter inference in cosmology and focus on when the graphical profile likelihood construction gives meaningful constraints, i.e. confidence intervals with correct coverage. This construction rests on the assumption of the asymptotic limit of a large data set such as in Wilks' theorem. We assess the validity of this assumption in the context of three cosmological models with Planck 2018 Plik_lite data: While our tests for the $Λ$CDM model indicate that the profile likelihood method gives correct coverage, $Λ$CDM with the sum of neutrino masses as a free parameter appears consistent with a Gaussian near a boundary motivating the use of the boundary-corrected or Feldman-Cousins graphical method; for $w_0$CDM with the equation of state of dark energy, $w_0$, as a free parameter, we find indication of a violation of the assumptions. Finally, we compare frequentist and Bayesian constraints of these models. Our results motivate care when using the graphical profile likelihood method in cosmology. Along with this paper, we publish our profile-likelihood code "pinc".

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。

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