任意测量几何中两点和三点关联函数矩的协方差矩阵估计
Estimating Covariance Matrices for Two- and Three-Point Correlation Function Moments in Arbitrary Survey Geometries
摘要：
我们提出的配置空间估计的自协方差和互协方差的两点和三点关联函数（2PCF和3PCF）在一般的调查几何。这些是在高斯极限中导出的（将高阶关联函数设置为零），但是对于任意非线性2PCF（其可以从勘测本身估计），其中包括散粒噪声重新缩放参数以捕获非高斯性。我们概括了以前的方法，包括勒让德矩通过几何校正函数校准测量对和三重计数。利用重要性抽样和随机粒子目录，我们可以估计模型协方差的分数所需的时间与模拟，获得估计与可忽略的采样噪声在$\sim 10$（$\sim 100$）CPU小时的2PCF（3PCF）自协方差。我们将结果与来自一套BOSS DR 12模拟的样本协方差进行比较，并发现矩阵具有良好的一致性，假设2PCF（3PCF）的散粒噪声重新缩放参数为$1.03$（$1.20$）。为了获得最强的约束宇宙学参数，我们必须使用多种统计在演唱会上，有强大的方法来衡量其协方差在低计算成本，因此是非常相关的即将到来的调查。
英文摘要：
We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher-order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogs, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in $\sim 10$ ($\sim 100$) CPU-hours for the 2PCF (3PCF) auto-covariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of $1.03$ ($1.20$) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.
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