Large Covariance Matrices: Smooth Models from the 2-Point Correlation Function

TL;DR

This paper presents a new method for estimating galaxy correlation function covariance matrices that significantly reduces computational noise and mock requirements by combining theoretical models with survey data calibration.

Contribution

The authors introduce a novel covariance estimation technique that combines simple theoretical models with survey data, reducing mock requirements and computational noise.

Findings

Model covariance matches mock covariance closely.

Requires fewer mocks than traditional methods.

Achieves noise reduction with ~1,000 CPU hours.

Abstract

We introduce a new method for estimating the covariance matrix for the galaxy correlation function in surveys of large-scale structure. Our method combines simple theoretical results with a realistic characterization of the survey to dramatically reduce noise in the covariance matrix. For example, with an investment of only ~1,000 CPU hours we can produce a model covariance matrix with noise levels that would otherwise require ~35,000 mocks. Non-Gaussian contributions to the model are calibrated against mock catalogs, after which the model covariance is found to be in impressive agreement with the mock covariance matrix. Since calibration of this method requires fewer mocks than brute force approaches, we believe that it could dramatically reduce the number of mocks required to analyse future surveys.