The 2-point correlation function covariance with fewer mocks

TL;DR

This paper introduces a fitted jackknife method to estimate the covariance of 2-point correlation functions accurately with significantly fewer mocks, extending applicability to denser galaxy samples and reducing computational costs.

Contribution

The authors develop a new fitted jackknife approach that accurately estimates covariance matrices with fewer mocks, outperforming the Mohammad-Percival correction especially for dense galaxy samples.

Findings

Fitted jackknife approach matches covariance accuracy with 25 mocks as well as traditional methods with over 1000 mocks.

The Mohammad-Percival correction introduces bias that increases with galaxy density.

Fewer mocks (by a factor of 40-60) are needed for reliable covariance estimation.

Abstract

We present an approach for accurate estimation of the covariance of 2-point correlation functions that requires fewer mocks than the standard mock-based covariance. This can be achieved by dividing a set of mocks into jackknife regions and fitting the correction term first introduced in Mohammad & Percival (2022), such that the mean of the jackknife covariances corresponds to the one from the mocks. This extends the model beyond the shot-noise limited regime, allowing it to be used for denser samples of galaxies. We test the performance of our fitted jackknife approach, both in terms of accuracy and precision, using lognormal mocks with varying densities and approximate EZmocks mimicking the DESI LRG and ELG samples in the redshift range of z = [0.8, 1.2]. We find that the Mohammad-Percival correction produces a bias in the 2-point correlation function covariance matrix that grows with number density and that our fitted jackknife approach does not. We also study the effect of the covariance on the uncertainty of cosmological parameters by performing a full-shape analysis. We find that our fitted jackknife approach based on 25 mocks is able to recover unbiased and as precise cosmological parameters as the ones obtained from a covariance matrix based on 1000 or 1500 mocks, while the Mohammad-Percival correction produces uncertainties that are twice as large. The number of mocks required to obtain an accurate estimation of the covariance for 2-point correlation function is therefore reduced by a factor of 40-60.