The Effect of Covariance Estimator Error on Cosmological Parameter Constraints

TL;DR

This paper demonstrates how errors in covariance matrix estimation from simulations can significantly inflate uncertainties in cosmological parameter constraints, emphasizing the importance of accurate covariance determination.

Contribution

It quantifies the impact of covariance estimator errors on parameter uncertainties, providing a formula relating the increase to the number of measurement bands and simulations.

Findings

Uncertainty in covariance matrices propagates to increased parameter errors.

Variance of parameters scales approximately as 1 + N_b/N_s.

Highlights the necessity for sufficient simulations in cosmological analyses.

Abstract

Extracting parameter constraints from cosmological observations requires accurate determination of the covariance matrix for use in the likelihood function. We show here that uncertainties in the elements of the covariance matrix propagate directly to increased uncertainties in cosmological parameters. When the covariance matrix is determined by simulations, the resulting variance of the each parameter increases by a factor of order $1+N_b/N_s$ where $N_b$ is the number of bands in the measurement and $N_s$ is the number of simulations.