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

Euclid Collaboration; E. Keihanen; V. Lindholm; P. Monaco; L. Blot; C. Carbone; K. Kiiveri; A. G. Sánchez; A. Viitanen; J. Valiviita; A. Amara; N. Auricchio; M. Baldi; D. Bonino; E. Branchini; M. Brescia; J. Brinchmann; S. Camera; V. Capobianco; J. Carretero; M. Castellano; S. Cavuoti; A. Cimatti; R. Cledassou; G. Congedo; L. Conversi; Y. Copin; L. Corcione; M. Cropper; A. Da Silva; H. Degaudenzi; M. Douspis; F. Dubath; C. A. J. Duncan; X. Dupac; S. Dusini; A. Ealet; S. Farrens; S. Ferriol; M. Frailis; E. Franceschi; M. Fumana; B. Gillis; H. Hoekstra; M. Kunz; P. Schneider; C. Sirignano; A. N. Taylor; E. A. Valentijn; Y. Wang; J. Weller

doi:10.1051/0004-6361/202244065

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

Euclid Collaboration, E. Keihanen, V. Lindholm, P. Monaco, L. Blot, C. Carbone, K. Kiiveri, A. G. Sánchez, A. Viitanen, J. Valiviita, A. Amara, N. Auricchio, M. Baldi, D. Bonino, E. Branchini, M. Brescia, J. Brinchmann, S. Camera, V. Capobianco, J. CarreteroM. Castellano, S. Cavuoti, A. Cimatti, R. Cledassou, G. Congedo, L. Conversi, Y. Copin, L. Corcione, M. Cropper, A. Da Silva, H. Degaudenzi, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, A. Ealet, S. Farrens, S. Ferriol, M. Frailis, E. Franceschi, M. Fumana, B. Gillis, H. Hoekstra, M. Kunz, P. Schneider, C. Sirignano, A. N. Taylor, E. A. Valentijn, Y. Wang, J. Weller

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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.

Original language	English
Article number	A129
Number of pages	17
Journal	Astronomy and Astrophysics
Volume	666
Issue number	October 2022
DOIs	https://doi.org/10.1051/0004-6361/202244065
Publication status	Published - 14-Oct-2022

Keywords

Cosmology: observations
Large-scale structure of Universe
Methods: data analysis
Methods: statistical

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10.1051/0004-6361/202244065Licence: CC BY

Euclid: Fast two-point correlation function covariance through linear constructionFinal publisher's version, 1.15 MBLicence: CC BY

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Euclid Collaboration, Keihanen, E., Lindholm, V., Monaco, P., Blot, L., Carbone, C., Kiiveri, K., Sánchez, A. G., Viitanen, A., Valiviita, J., Amara, A., Auricchio, N., Baldi, M., Bonino, D., Branchini, E., Brescia, M., Brinchmann, J., Camera, S., Capobianco, V., ... Weller, J. (2022). Euclid: Fast two-point correlation function covariance through linear construction. Astronomy and Astrophysics, 666(October 2022), Article A129. https://doi.org/10.1051/0004-6361/202244065

@article{18773573cf0c4f5cad1cb2eae8f68aea,

title = "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.",

keywords = "Cosmology: observations, Large-scale structure of Universe, Methods: data analysis, Methods: statistical",

author = "{Euclid Collaboration} and E. Keihanen and V. Lindholm and P. Monaco and L. Blot and C. Carbone and K. Kiiveri and S{\'a}nchez, {A. G.} and A. Viitanen and J. Valiviita and A. Amara and N. Auricchio and M. Baldi and D. Bonino and E. Branchini and M. Brescia and J. Brinchmann and S. Camera and V. Capobianco and J. Carretero and M. Castellano and S. Cavuoti and A. Cimatti and R. Cledassou and G. Congedo and L. Conversi and Y. Copin and L. Corcione and M. Cropper and {Da Silva}, A. and H. Degaudenzi and M. Douspis and F. Dubath and Duncan, {C. A. J.} and X. Dupac and S. Dusini and A. Ealet and S. Farrens and S. Ferriol and M. Frailis and E. Franceschi and M. Fumana and B. Gillis and H. Hoekstra and M. Kunz and P. Schneider and C. Sirignano and Taylor, {A. N.} and Valentijn, {E. A.} and Y. Wang and J. Weller",

note = "Funding 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{\textquoteright}Etudes Spatiales, the Deutsches Zentrum f{\"u}r Luft- und Raumfahrt, the Danish Space Research Institute, the Funda{\c c}{\~a}o para a Ci{\^e}ncia 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 ). Publisher Copyright: {\textcopyright} ",

year = "2022",

month = oct,

day = "14",

doi = "10.1051/0004-6361/202244065",

language = "English",

volume = "666",

journal = "Astronomy and Astrophysics",

issn = "0004-6361",

publisher = " EDP Sciences",

number = "October 2022",

}

Euclid Collaboration, Keihanen, E, Lindholm, V, Monaco, P, Blot, L, Carbone, C, Kiiveri, K, Sánchez, AG, Viitanen, A, Valiviita, J, Amara, A, Auricchio, N, Baldi, M, Bonino, D, Branchini, E, Brescia, M, Brinchmann, J, Camera, S, Capobianco, V, Carretero, J, Castellano, M, Cavuoti, S, Cimatti, A, Cledassou, R, Congedo, G, Conversi, L, Copin, Y, Corcione, L, Cropper, M, Da Silva, A, Degaudenzi, H, Douspis, M, Dubath, F, Duncan, CAJ, Dupac, X, Dusini, S, Ealet, A, Farrens, S, Ferriol, S, Frailis, M, Franceschi, E, Fumana, M, Gillis, B, Hoekstra, H, Kunz, M, Schneider, P, Sirignano, C, Taylor, AN, Valentijn, EA, Wang, Y & Weller, J 2022, 'Euclid: Fast two-point correlation function covariance through linear construction', Astronomy and Astrophysics, vol. 666, no. October 2022, A129. https://doi.org/10.1051/0004-6361/202244065

TY - JOUR

T1 - Euclid: Fast two-point correlation function covariance through linear construction

AU - Euclid Collaboration

AU - Keihanen, E.

AU - Lindholm, V.

AU - Monaco, P.

AU - Blot, L.

AU - Carbone, C.

AU - Kiiveri, K.

AU - Sánchez, A. G.

AU - Viitanen, A.

AU - Valiviita, J.

AU - Amara, A.

AU - Auricchio, N.

AU - Baldi, M.

AU - Bonino, D.

AU - Branchini, E.

AU - Brescia, M.

AU - Brinchmann, J.

AU - Camera, S.

AU - Capobianco, V.

AU - Carretero, J.

AU - Castellano, M.

AU - Cavuoti, S.

AU - Cimatti, A.

AU - Cledassou, R.

AU - Congedo, G.

AU - Conversi, L.

AU - Copin, Y.

AU - Corcione, L.

AU - Cropper, M.

AU - Da Silva, A.

AU - Degaudenzi, H.

AU - Douspis, M.

AU - Dubath, F.

AU - Duncan, C. A. J.

AU - Dupac, X.

AU - Dusini, S.

AU - Ealet, A.

AU - Farrens, S.

AU - Ferriol, S.

AU - Frailis, M.

AU - Franceschi, E.

AU - Fumana, M.

AU - Gillis, B.

AU - Hoekstra, H.

AU - Kunz, M.

AU - Schneider, P.

AU - Sirignano, C.

AU - Taylor, A. N.

AU - Valentijn, E. A.

AU - Wang, Y.

AU - Weller, J.

N1 - Funding 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 ). Publisher Copyright: ©

PY - 2022/10/14

Y1 - 2022/10/14

N2 - 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.

AB - 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.

KW - Cosmology: observations

KW - Large-scale structure of Universe

KW - Methods: data analysis

KW - Methods: statistical

U2 - 10.1051/0004-6361/202244065

DO - 10.1051/0004-6361/202244065

M3 - Article

AN - SCOPUS:85141011741

SN - 0004-6361

VL - 666

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

IS - October 2022

M1 - A129

ER -

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

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