Performance of internal Covariance Estimators for Cosmic Shear Correlation Functions

TL;DR

This paper evaluates the effectiveness of internal covariance estimators like jackknife in cosmic shear analysis, demonstrating they can reliably approximate true uncertainties in cosmological parameters using realistic simulations.

Contribution

It provides a detailed assessment of internal covariance estimators for cosmic shear, showing they can effectively approximate true covariance and uncertainties in large-scale structure surveys.

Findings

Internal covariance estimators can achieve a good bias-variance trade-off.

Internally estimated covariances recover over 85% of the true parameter volume.

Uncertainty estimates from internal methods are about 90% of the true uncertainties.

Abstract

Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic shear two-point statistics. We demonstrate how to use log-normal simulations of the convergence field and the corresponding shear field to carry out realistic tests of internal covariance estimators and find that most estimators such as jackknife or sub-sample covariance can reach a satisfactory compromise between bias and variance of the estimated covariance. In a forecast for the complete, 5-year DES survey we show that internally estimated covariance matrices can provide a large fraction of the true uncertainties on cosmological parameters in a 2D cosmic shear analysis. The volume inside contours of constant likelihood in the $\Omega_m$-$\sigma_8$ plane as measured with internally estimated covariance matrices is on average $\gtrsim 85\%$ of the volume derived from the true covariance matrix. The uncertainty on the parameter combination $\Sigma_8 \sim \sigma_8 \Omega_m^{0.5}$ derived from internally estimated covariances is $\sim 90\%$ of the true uncertainty.