标题： 稀疏协方差：在使用天空中离散观测样本估计相关函数时的不确定性来源 显示英文标题

标题： Sparsity covariance: a source of uncertainty when estimating correlation functions with a discrete sample of observations in the sky

摘要： 宇宙学观测结果严重依赖于诸如两点关联函数之类的总结统计量。 在许多实际情况下（例如弱引力透镜宇宙剪切），这些关联函数是从天空中随机分布的有限离散测量样本中估计得到的。 因此，结果不可避免地依赖于当前的样本，无论是否存在任何实验噪声。 这种样本依赖性是宇宙学观测结果的一个不确定性来源，我称之为稀疏性协方差。 本文提出了一个数学定义和一种通用方法来计算稀疏性协方差。 然后将其应用于宇宙剪切的具体情况，表明稀疏性协方差主要增强了形状噪声，其幅度由星系的表观椭圆率而非其固有椭圆率决定。 一般来说，当样本中单个测量的信噪比与1相当或大于1时，稀疏性协方差是不可忽略的。 显示英文摘要

摘要： Cosmological observables rely heavily on summary statistics such as two-point correlation functions. In many practical cases (e.g. the weak-lensing cosmic shear), those correlation functions are estimated from a finite, discrete sample of measurements that are randomly distributed in the sky. The result then inevitably depends on the sample at hand, regardless of any experimental noise. This sample dependence is a source of uncertainty for cosmological observables which I call sparsity covariance. This article proposes a mathematical definition and a generic method to compute sparsity covariance. It is then applied to the concrete case of cosmic shear, showing that sparsity covariance mostly enhances shape noise, whose amplitude is determined by the apparent ellipticity of galaxies rather than their intrinsic ellipticity. In general, sparsity covariance is non-negligible when the signal-to-noise ratio of individual measurements in the sample is comparable to, or larger than, unity.