A fast and reliable method for the comparison of covariance matrices

TL;DR

This paper introduces a fast, reliable method for comparing large covariance matrices in cosmology by focusing on relevant data portions and using Monte Carlo simulations, significantly reducing computational costs.

Contribution

The paper presents a novel, efficient approach to compare covariance matrices using compression schemes and Monte Carlo simulations, saving substantial computational resources.

Findings

Method agrees with full analysis within 2.6% parameter uncertainty

Reduces computational cost by approximately 100 times

Applicable to covariance matrices in large cosmological data sets

Abstract

Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements grows as the square of the size of the data vector. The most straightforward way of comparing these matrices, in terms of their ability to produce parameter constraints, involves a full cosmological analysis, which can be very computationally expensive. Using the concept and construction of compression schemes, which have become increasingly popular, we propose a fast and reliable way of comparing covariance matrices. The basic idea is to focus only on the portion of the covariance matrix that is relevant for the parameter constraints and quantify, via a fast Monte Carlo simulation, the difference of a second candidate matrix from the baseline one. To test this method, we apply it to two covariance matrices that were used to analyse the cosmic shear measurements for the Dark Energy Survey Year 1. We found that the uncertainties on the parameters change by 2.6%, a figure in agreement with the full cosmological analysis. While our approximate method cannot replace a full analysis, it may be useful during the development and validation of codes that estimate covariance matrices. Our method takes roughly 100 times less CPUh than a full cosmological analysis.