Decorrelating the errors of the galaxy correlation function with compact transformation matrices

Citation:

Yuan S, Eisenstein DJ. Decorrelating the errors of the galaxy correlation function with compact transformation matrices. Monthly Notices of the Royal Astronomical Society [Internet]. 2019;486 :708-724.

Date Published:

June 01, 2019

Abstract:

Covariance matrix estimation is a persistent challenge for cosmology,often requiring a large number of synthetic mock catalogues. The off-diagonal components of the covariance matrix also make it difficult toshow representative error bars on the 2-point correlation function(2PCF) since errors computed from the diagonal values of the covariancematrix greatly underestimate the uncertainties. We develop a routine fordecorrelating the projected and anisotropic 2PCF with simple and scale-compact transformations on the 2PCF. These transformation matrices aremodelled after the Cholesky decomposition and the symmetric square rootof the Fisher matrix. Using mock catalogues, we show that thetransformed projected and anisotropic 2PCF recover the same structure asthe original 2PCF while producing largely decorrelated error bars.Specifically, we propose simple Cholesky-based transformation matricesthat suppress the off-diagonal covariances on the projected 2PCF by {̃ }95{{ per cent}} and that on the anisotropic 2PCF by {̃ } 87{{ percent}}. These transformations also serve as highly regularized models ofthe Fisher matrix, compressing the degrees of freedom so that one canfit for the Fisher matrix with a much smaller number of mocks.

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