Dark Energy Survey Year 3 Results: Covariance Modelling and its Impact
  on Parameter Estimation and Quality of Fit
  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 $5\%$.
