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arXiv 2203.16285astro-ph.CO
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蒙特卡罗分析中边缘化影响的快速检验及其在宇宙学中的应用

A fast test to assess the impact of marginalization in Monte Carlo analyses, and its application to cosmology

Adrià Gómez-Valent

摘要:

蒙特卡罗(MC)算法通常用于探索受数据约束的高维参数空间。这些分析的输出中获得的所有统计信息都包含在马尔可夫链中,需要对其进行处理和解释。边缘化技术允许我们消化这些链并计算感兴趣的参数子集的后验分布。特别是,它让我们在二维平面上绘制置信区域,并获得各个参数的约束。然而,众所周知,边缘化的结果可能会受到体积效应的影响,这可能会给我们的结论带来不可忽视的偏差。在文献中几乎没有研究过这些效应的影响。在本文中,我们首先说明了这个问题,通过一个非常清晰和简单的例子在两个维度上,并建议使用的轮廓分布(PD)作为一种补充工具,直接从MC链检测边缘化偏见。我们将我们的方法应用到四个宇宙学模型:标准$Λ$ CDM,早期暗能量,耦合暗能量和具有宇宙学常数的Brans-Dicke模型。我们讨论了体积效应对每个模型和宇宙学张力的影响,使用完整的普朗克2018可能性,Ia型超新星的万神殿汇编和重子声学振荡的数据。我们的测试是非常有效的,可以很容易地应用到任何MC研究。它使我们能够估计的PD在一个可笑的计算成本,不仅为主要的宇宙学参数,但也为滋扰和衍生的,并评估需要进行更深入的分析与精确计算的PD。

英文摘要:

Monte Carlo (MC) algorithms are commonly employed to explore high-dimensional parameter spaces constrained by data. All the statistical information obtained in the output of these analyses is contained in the Markov chains, which one needs to process and interpret. The marginalization technique allows us to digest these chains and compute the posterior distributions for the parameter subsets of interest. In particular, it lets us draw confidence regions in two-dimensional planes, and get the constraints for the individual parameters. It is very well known, though, that the marginalized results can suffer from volume effects, which can introduce a non-negligible bias into our conclusions. The impact of these effects are barely studied in the literature. In this paper we first illustrate the problem through a very clear and simple example in two dimensions, and suggest the use of the profile distributions (PDs) as a complementary tool to detect marginalization biases directly from the MC chains. We apply our method to four cosmological models: the standard $Λ$CDM, early dark energy, coupled dark energy and the Brans-Dicke model with a cosmological constant. We discuss the impact of the volume effects on each model and the cosmological tensions, using the full Planck 2018 likelihood, the Pantheon compilation of supernovae of Type Ia and data on baryon acoustic oscillations. Our test is very efficient and can be easily applied to any MC study. It allows us to estimate the PDs at a derisory computational cost not only for the main cosmological parameters, but also for the nuisance and derived ones, and to assess the need to perform a more in-depth analysis with the exact computation of the PDs.

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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