Errors on errors - Estimating cosmological parameter covariance

TL;DR

This paper reviews recent methods to quantify and correct biases and variances in cosmological parameter errors caused by finite data covariance estimations, crucial for precise cosmological analyses.

Contribution

It provides a comprehensive review of recent techniques to address biases and variances in covariance matrix estimation for cosmological data analysis.

Findings

Finite sample sizes introduce biases in covariance estimates.

Bias correction methods can improve parameter error estimates.

Accurate covariance estimation is essential for reliable cosmological inferences.

Abstract

Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.