Cosmic shear covariance: the log-normal approximation
Cosmic shear covariance: the log-normal approximation
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DOI：
10.1051/0004-6361/201117294
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发表时间：
2011-05
影响因子：
6.5
通讯作者：
S. Hilbert;J. Hartlap;P. Schneider
中科院分区：
文献类型：
--
作者：
S. Hilbert;J. Hartlap;P. Schneider
上下文。准确估计从宇宙剪切测量推断出的宇宙学参数的误差，需要准确估计宇宙剪切相关函数的协方差。目标。我们寻求与基于正态(高斯)统计量的常见近似一样易于使用的宇宙切变协方差的近似，但产生更准确的协方差矩阵和参数误差。方法：研究方法。在基本收敛场服从对数正态分布的假设下，我们推导出了宇宙切变协方差的表达式。我们还通过仅保留超出正态统计的最重要的项，导出了这种对数正态近似的简化版本。我们使用弱透镜的数值模拟来研究文献中提出的正态、对数正态和简化的对数正态近似以及对正态近似的经验修正在多大程度上再现了宇宙剪切测量的剪切协方差。我们还调查了从这类调查中推断出的宇宙学参数的结果置信域。结果。我们发现，正态近似大大低估了宇宙剪切协方差和推断的参数置信域，特别是对于小视场和大星系密度的观测，而且对于非常广泛的观测也是如此。相比之下，对数正态近似产生更真实的协方差和置信域，但也需要计算稍微复杂的表达式。然而，简化的对数正态近似虽然像正态近似一样简单，但产生的置信度区域几乎与对数正态近似得到的置信度区域一样精确。对正态近似的经验修正并不比(简化的)对数正态近似产生更准确的协方差和置信域。此外，在某些情况下，它们不能产生正半定数据协方差矩阵，使得它们不能用于参数估计。结论。对于参数估计和参数误差预测，应使用对数正态或简化对数正态近似，而不是正态近似。更一般地，对宇宙切变协方差的任何近似都应该确保数据协方差矩阵是正(半)定的。
Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims. We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods. We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results. We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them unusable for parameter estimation. Conclusions. The log-normal or simplified log-normal approximation should be used in favour of the normal approximation for parameter estimation and parameter error forecasts. More generally, any approximation to the cosmic shear covariance should ensure a positive-(semi)definite data covariance matrix.