Published October 2022 | Version public
Journal Article

Euclid: Fast two-point correlation function covariance through linear construction

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.

Additional Information

The 2PCF computations were done at the Euclid Science Data Center Finland (SDC-FI, urn:nbn:fi:research-infras-2016072529), for whose computational resources we thank CSC – IT Center for Science, the Finnish Grid and Cloud Computing Infrastructure (FGCI, urn:nbn:fi:research-infras-2016072533), and the Academy of Finland grant 292882. This work was supported by the Academy of Finland grant 295113. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Academy of Finland, the Agenzia Spaziale Italiana, the Belgian Science Policy, the Canadian Euclid Consortium, the French Centre National d'Etudes Spatiales, the Deutsches Zentrum für Luft- und Raumfahrt, the Danish Space Research Institute, the Fundação para a Ciência e a Tecnologia, the Ministerio de Economia y Competitividad, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Romanian Space Agency, the State Secretariat for Education, Research and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid web site (http://www.euclid-ec.org).

Additional details

Identifiers

Eprint ID
117753
Resolver ID
CaltechAUTHORS:20221107-999291600.24

Funding

Academy of Finland
292882
Academy of Finland
295113
Agenzia Spaziale Italiana (ASI)
Belgian Federal Science Policy Office (BELSPO)
Canadian Euclid Consortium
Centre National de la Recherche Scientifique (CNRS)
Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Danish Space Research Institute
Fundação para a Ciência e Tecnologia (FCT)
Ministerio de Economía, Industria y Competitividad (MINECO)
NASA
National Astronomical Observatory of Japan
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)
Norwegian Space Agency
Romanian Space Agency
State Secretariat for Education, Research and Innovation (SERI)
Swiss Space Office (SSO)
United Kingdom Space Agency (UKSA)

Dates

Created
2022-11-18
Created from EPrint's datestamp field
Updated
2022-11-19
Created from EPrint's last_modified field

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