Fitting covariance matrix models to simulations

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 theoretical model for the matrix exists, parameters can fit with many fewer simulations. We write likelihood-based method performing such fit. demonstrate how tested by examining appropriate $\chi^2$ distributions show that if has amplitude freedom, expectation value second moment distribution wrong will always larger than one using true matrix. By combining these steps together, we provide way producing covariances without ever requiring running our on two examples. First, measure two-point correlation function halos set $10000$ mock halo catalogs. build $2$ free parameters, which procedure. The resulting best-fit obtained just $100$ simulation proves as built full set. also test setup where is measuring bispectrum thousands triangles same mocks. block diagonal an improvement over Gaussian covariance. Our passes only partially this case, signaling insufficient even but significantly improves one.