Estimating the power spectrum covariance matrix with fewer mock samples

TL;DR

This paper introduces a seven-parameter model to estimate the power spectrum covariance matrix from galaxy survey data, reducing the need for large mock samples and improving accuracy over traditional sample covariance methods.

Contribution

A theoretically justified, few-parameter model for covariance matrix estimation that requires fewer mock samples and converges faster than traditional methods.

Findings

A seven-parameter model fits BOSS DR11 covariance matrices effectively.

The model outperforms sample covariance with fewer mocks.

Only about 100 mocks are needed for full convergence.

Abstract

The covariance matrices of power-spectrum (P(k)) measurements from galaxy surveys are difficult to compute theoretically. The current best practice is to estimate covariance matrices by computing a sample covariance of a large number of mock catalogues. The next generation of galaxy surveys will require thousands of large volume mocks to determine the covariance matrices to desired accuracy. The errors in the inverse covariance matrix are larger and scale with the number of P(k) bins, making the problem even more acute. We develop a method of estimating covariance matrices using a theoretically justified, few-parameter model, calibrated with mock catalogues. Using a set of 600 BOSS DR11 mock catalogues, we show that a seven parameter model is sufficient to fit the covariance matrix of BOSS DR11 P(k) measurements. The covariance computed with this method is better than the sample covariance at any number of mocks and only ~100 mocks are required for it to fully converge and the inverse covariance matrix converges at the same rate. This method should work equally well for the next generation of galaxy surveys, although a demand for higher accuracy may require adding extra parameters to the fitting function.