用归一化流近似非高斯贝叶斯划分：统计、推断及宇宙学应用
Approximating non-Gaussian Bayesian partitions with normalising flows: statistics, inference and application to cosmology
AI总结：
本文利用归一化流简化贝叶斯推断中的MCMC采样，计算非高斯分布的划分函数并求后验解析式，应用于宇宙学参数推断，基于超新星数据估计物质密度和暗能量参数。
摘要：
本文的主题是利用归一化流（一种能够构建高斯与非高斯随机分布之间可逆且可微变换的机器学习方法）来简化贝叶斯统计推断中使用的马尔可夫链蒙特卡洛采样。我们使用归一化流计算非高斯分布的贝叶斯划分函数，并展示归一化流如何用于寻找超越高斯极限的后验分布的解析表达式。流在划分函数本身的数值评估以及累积量和信息熵方面具有优势。我们演示了归一化流与贝叶斯划分相结合如何用于宇宙学中的推断问题，并将其应用于基于超新星数据的物质密度 $Ω_m$ 和暗能量状态方程参数 $w_0$ 的后验分布。
英文摘要：
Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable transformation between Gaussian and non-Gaussian random distributions. We use normalising flows to compute Bayesian partition functions for non-Gaussian distributions and show how normalising flows can be employed in finding analytical expressions for posterior distributions beyond the Gaussian limit. Flows offer advantages for the numerical evaluation of the partition function itself, as well as for cumulants and for the information entropy. We demonstrate how normalising flows in conjunction with Bayes partitions can be used in inference problems in cosmology and apply them to the posterior distribution for the matter density $Ω_m$ and a dark energy equation of state parameter $w_0$ on the basis of supernova data.
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。
