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• W4311761947 abstract "Data analysis in cosmology requires reliable covariance matrices. Covariance matrices derived from numerical simulations often require a very large number of realizations to be accurate. When a theoretical model for the covariance matrix exists, the parameters of the model can often be fit with many fewer simulations. We write a likelihood-based method for performing such a fit. We demonstrate how a model covariance matrix can be tested by examining the appropriate $chi^2$ distributions from simulations. We show that if model covariance has amplitude freedom, the expectation value of second moment of $chi^2$ distribution with a wrong covariance matrix will always be larger than one using the true covariance matrix. By combining these steps together, we provide a way of producing reliable covariances without ever requiring running a large number of simulations. We demonstrate our method on two examples. First, we measure the two-point correlation function of halos from a large set of $10000$ mock halo catalogs. We build a model covariance with $2$ free parameters, which we fit using our procedure. The resulting best-fit model covariance obtained from just $100$ simulation realizations proves to be as reliable as the numerical covariance matrix built from the full $10000$ set. We also test our method on a setup where the covariance matrix is large by measuring the halo bispectrum for thousands of triangles for the same set of mocks. We build a block diagonal model covariance with $2$ free parameters as an improvement over the diagonal Gaussian covariance. Our model covariance passes the $chi^2$ test only partially in this case, signaling that the model is insufficient even using free parameters, but significantly improves over the Gaussian one." @default.
• W4311761947 created "2022-12-28" @default.
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• W4311761947 date "2022-12-01" @default.
• W4311761947 modified "2023-10-01" @default.
• W4311761947 title "Fitting covariance matrix models to simulations" @default.
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• W4311761947 doi "https://doi.org/10.1088/1475-7516/2022/12/022" @default.
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