论文标题
快速测试评估边缘化在蒙特卡洛分析中的影响及其在宇宙学上的应用
A fast test to assess the impact of marginalization in Monte Carlo analyses, and its application to cosmology
论文作者
论文摘要
蒙特卡洛（MC）算法通常用于探索受数据约束的高维参数空间。这些分析输出中获得的所有统计信息都包含在马尔可夫链中，这需要处理和解释。边缘化技术使我们能够消化这些链并计算感兴趣的参数子集的后验分布。特别是，它使我们能够在二维平面中绘制置信区，并获得单个参数的约束。但是，众所周知，边缘化的结果可能会遭受体积影响，这可能会引入我们的结论中不可忽略的偏见。这些影响的影响在文献中几乎没有研究。在本文中，我们首先通过在两个维度中的一个非常清晰，简单的示例来说明问题，并建议将配置文件分布（PDS）用作直接从MC链中检测边缘化偏见的补充工具。我们将方法应用于四个宇宙学模型：标准$λ$ CDM，早期的暗能量，耦合的暗能量和带有宇宙常数的Brans-Dicke模型。我们使用完整的Planck 2018可能性，IA型超新星的万神殿汇编以及对巴里昂声学振荡的数据，讨论了体积影响对每个模型和宇宙张力的影响。我们的测试非常有效，可以轻松地应用于任何MC研究。它使我们能够不仅针对主要的宇宙参数，而且对于滋扰和衍生的估算PDS估算PDS，并评估使用PDS的确切计算进行更深入的分析的需求。
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.
