Decorrelating the errors of the galaxy correlation function with compact transformation matrices. (arXiv:1901.05019v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Yuan_S/0/1/0/all/0/1">Sihan Yuan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Eisenstein_D/0/1/0/all/0/1">Daniel J. Eisenstein</a>
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 to show
representative error bars on the 2PCF, since errors computed from the diagonal
values of the covariance matrix greatly underestimate the uncertainties. We
develop a routine for decorrelating the projected and anisotropic 2PCF with
simple and scale-compact transformations on the 2PCF. These transformation
matrices are modeled after the Cholesky decomposition and the symmetric square
root of the Fisher matrix. Using mock catalogues, we show that the transformed
projected and anisotropic 2PCF recover the same structure as the original 2PCF,
while producing largely decorrelated error bars. Specifically, we propose
simple Cholesky based transformation matrices that suppress the off-diagonal
covariances on the projected 2PCF by ~95% and that on the anisotropic 2PCF by
~87%. These transformations also serve as highly regularized models of the
Fisher matrix, compressing the degrees of freedom so that one can fit for the
Fisher matrix with a much smaller number of mocks.
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 to show
representative error bars on the 2PCF, since errors computed from the diagonal
values of the covariance matrix greatly underestimate the uncertainties. We
develop a routine for decorrelating the projected and anisotropic 2PCF with
simple and scale-compact transformations on the 2PCF. These transformation
matrices are modeled after the Cholesky decomposition and the symmetric square
root of the Fisher matrix. Using mock catalogues, we show that the transformed
projected and anisotropic 2PCF recover the same structure as the original 2PCF,
while producing largely decorrelated error bars. Specifically, we propose
simple Cholesky based transformation matrices that suppress the off-diagonal
covariances on the projected 2PCF by ~95% and that on the anisotropic 2PCF by
~87%. These transformations also serve as highly regularized models of the
Fisher matrix, compressing the degrees of freedom so that one can fit for the
Fisher matrix with a much smaller number of mocks.
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