标题： 利用互信息评估用于宇宙学推理的总结统计量 显示英文标题

标题： Evaluating Summary Statistics with Mutual Information for Cosmological Inference

摘要： 压缩观测数据并准确估计物理参数的能力在很大程度上依赖于信息量丰富的摘要统计量。本文中，我们介绍了互信息（MI）作为评估推理任务中摘要统计量质量的一种方法。互信息可以评估摘要的充分性，并提供比较的定量基础。我们建议使用Barber-Agakov下界和基于归一化流的变分分布来估计MI。为了证明我们方法的有效性，我们在平方公里阵列21厘米观测的模拟图像中推断再电离参数的背景下，比较了三种不同的摘要统计量（即功率谱、双谱和散射变换）。我们发现这种方法能够正确评估不同摘要统计量的信息量，并允许我们为推理任务选择最佳的统计集。 显示英文摘要

摘要： The ability to compress observational data and accurately estimate physical parameters relies heavily on informative summary statistics. In this paper, we introduce the use of mutual information (MI) as a means of evaluating the quality of summary statistics in inference tasks. MI can assess the sufficiency of summaries, and provide a quantitative basis for comparison. We propose to estimate MI using the Barber-Agakov lower bound and normalizing flow based variational distributions. To demonstrate the effectiveness of our method, we compare three different summary statistics (namely the power spectrum, bispectrum, and scattering transform) in the context of inferring reionization parameters from mock images of 21~cm observations with Square Kilometre Array. We find that this approach is able to correctly assess the informativeness of different summary statistics and allows us to select the optimal set of statistics for inference tasks.