Keihänen, E. and Lindholm, V. and Monaco, P. and Blot, L. and Carbone, C. and Kiiveri, K. and Sánchez, A. G. and Viitanen, A. and Valiviita, J. and Amara, A. and Auricchio, N. and Baldi, M. and Bonino, D. and Branchini, E. and Brescia, M. and Brinchmann, J. and Camera, S. and Capobianco, V. and Carretero, J. and Castellano, M. and Cavuoti, S. and Cimatti, A. and Cledassou, R. and Congedo, G. and Conversi, L. and Copin, Y. and Corcione, L. and Cropper, M. and Da Silva, A. and Degaudenzi, H. and Douspis, M. and Dubath, F. and Duncan, C. A. J. and Dupac, X. and Dusini, S. and Ealet, A. and Farrens, S. and Ferriol, S. and Frailis, M. and Franceschi, E. and Fumana, M. and Gillis, B. and Giocoli, C. and Grazian, A. and Grupp, F. and Guzzo, L. and Haugan, S. V. H. and Hoekstra, H. and Holmes, W. and Hormuth, F. and Jahnke, K. and Kümmel, M. and Kermiche, S. and Kiessling, A and Kitching, T. and Kunz, M. and Kurki-Suonio, H. and Ligori, S. and Lilje, P. B. and Lloro, I. and Maiorano, E. and Mansutti, O. and Marggraf, O. and Marulli, F. and Massey, R. and Melchior, M. and Meneghetti, M. and Meylan, G. and Moresco, M. and Morin, B. and Moscardini, L. and Munari, E. and Niemi, S. M. and Padilla, C. and Paltani, S. and Pasian, F. and Pedersen, K. and Pettorino, V. and Pires, S. and Polenta, G. and Poncet, M. and Popa, L. and Raison, F. and Renzi, A. and Rhodes, J. and Romelli, E. and Saglia, R. and Sartoris, B. and Schneider, P. and Schrabback, T. and Secroun, A. and Seidel, G. and Sirignano, C. and Sirri, G. and Stanco, L. and Surace, C. and Tallada-Crespí, P. and Tavagnacco, D. and Taylor, A. N. and Tereno, I. and Toledo-Moreo, R. and Torradeflot, F. and Valentijn, E. A. and Valenziano, L. and Vassallo, T. and Wang, Y. and Weller, J. and Zamorani, G. and Zoubian, J. and Andreon, S. and Maino, D. and de la Torre, S. (2022) Euclid: Fast two-point correlation function covariance through linear construction. Astronomy and Astrophysics, 666 . Art. No. A129. ISSN 0004-6361. doi:10.1051/0004-6361/202244065. https://resolver.caltech.edu/CaltechAUTHORS:20221107-999291600.24
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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.
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| 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). | ||||||||||||||||||||||||||||||||||||||
| Group: | Infrared Processing and Analysis Center (IPAC) | ||||||||||||||||||||||||||||||||||||||
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| DOI: | 10.1051/0004-6361/202244065 | ||||||||||||||||||||||||||||||||||||||
| Record Number: | CaltechAUTHORS:20221107-999291600.24 | ||||||||||||||||||||||||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221107-999291600.24 | ||||||||||||||||||||||||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||||||||||||||||||||||
| ID Code: | 117753 | ||||||||||||||||||||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||||||||||||||||||||
| Deposited By: | Research Services Depository | ||||||||||||||||||||||||||||||||||||||
| Deposited On: | 18 Nov 2022 21:39 | ||||||||||||||||||||||||||||||||||||||
| Last Modified: | 19 Nov 2022 00:05 |
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