Keihänen, E;
Lindholm, V;
Monaco, P;
Blot, L;
Carbone, C;
Kiiveri, K;
Sánchez, AG;
... De la Torre, S; + view all
(2022)
Euclid: Fast two-point correlation function covariance through linear construction.
Astronomy & Astrophysics
, 666
, Article A129. 10.1051/0004-6361/202244065.
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Abstract
We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy–Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (random-to-data objects’ ratio M ≫ 1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs with a size of M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range r = 20 − 200 h−1 Mpc. With M = 50 and with 2 h−1 Mpc bins, the theoretical speedup of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and present a formula for the covariance of covariance.
| Type: | Article |
|---|---|
| Title: | Euclid: Fast two-point correlation function covariance through linear construction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/0004-6361/202244065 |
| Publisher version: | https://doi.org/10.1051/0004-6361/202244065 |
| Language: | English |
| Additional information: | Copyright © E. Keihänen et al. 2022. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | cosmology: observations; large-scale structure of Universe; methods: data analysis; methods: statistical |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10159381 |
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