Dark Energy Survey Year 3 Results: Covariance Modelling and its Impact on Parameter Estimation and Quality of Fit

TL;DR

This paper validates a covariance matrix model for DES-Y3 data analysis, demonstrating its robustness and quantifying the impact of various approximations on parameter estimation and fit quality.

Contribution

It introduces and tests a comprehensive covariance modeling approach for DES-Y3, including new ansatzes and an approximate scheme for survey area effects.

Findings

Covariance model is robust with minimal impact on fit and parameters.

Largest impact from $f_{sky}$ approximation increases chi-squared by 3.7%.

Parameter estimation scatter increases by 3-5% due to model evaluation uncertainties.

Abstract

We describe and test the fiducial covariance matrix model for the combined 2-point function analysis of the Dark Energy Survey Year 3 (DES-Y3) dataset. Using a variety of new ansatzes for covariance modelling and testing we validate the assumptions and approximations of this model. These include the assumption of a Gaussian likelihood, the trispectrum contribution to the covariance, the impact of evaluating the model at a wrong set of parameters, the impact of masking and survey geometry, deviations from Poissonian shot-noise, galaxy weighting schemes and other, sub-dominant effects. We find that our covariance model is robust and that its approximations have little impact on goodness-of-fit and parameter estimation. The largest impact on best-fit figure-of-merit arises from the so-called $f_{\mathrm{sky}}$ approximation for dealing with finite survey area, which on average increases the $\chi^2$ between maximum posterior model and measurement by $3.7\%$ ($\Delta \chi^2 \approx 18.9$). Standard methods to go beyond this approximation fail for DES-Y3, but we derive an approximate scheme to deal with these features. For parameter estimation, our ignorance of the exact parameters at which to evaluate our covariance model causes the dominant effect. We find that it increases the scatter of maximum posterior values for $\Omega_m$ and $\sigma_8$ by about $3\%$ and for the dark energy equation of state parameter by about $5\%$.