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

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.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Keihänen, E.0000-0003-1804-7715
Carbone, C.0000-0003-0125-3563
Sánchez, A. G.0000-0003-1198-831X
Valiviita, J.0000-0001-6225-3693
Auricchio, N.0000-0003-4444-8651
Baldi, M.0000-0003-4145-1943
Bonino, D.0000-0002-3336-9977
Branchini, E.0000-0002-0808-6908
Brescia, M.0000-0001-9506-5680
Brinchmann, J.0000-0003-4359-8797
Camera, S.0000-0003-3399-3574
Capobianco, V.0000-0002-3309-7692
Carretero, J.0000-0002-3130-0204
Castellano, M.0000-0001-9875-8263
Cavuoti, S.0000-0002-3787-4196
Cimatti, A.0000-0002-4409-5633
Cledassou, R.0000-0002-8313-2230
Congedo, G.0000-0003-2508-0046
Conversi, L.0000-0002-6710-8476
Copin, Y.0000-0002-5317-7518
Corcione, L.0000-0002-6497-5881
Cropper, M.0000-0003-4571-9468
Dubath, F.0000-0002-6533-2810
Dusini, S.0000-0002-1128-0664
Farrens, S.0000-0002-9594-9387
Frailis, M.0000-0002-7400-2135
Franceschi, E.0000-0002-0585-6591
Gillis, B.0000-0002-4478-1270
Giocoli, C.0000-0002-9590-7961
Grupp, F.0000-0001-7300-9303
Hoekstra, H.0000-0002-0641-3231
Jahnke, K.0000-0003-3804-2137
Kermiche, S.0000-0002-0302-5735
Kiessling, A0000-0002-2590-1273
Kitching, T.0000-0002-4061-4598
Kunz, M.0000-0003-1676-6126
Kurki-Suonio, H.0000-0002-4618-3063
Ligori, S.0000-0003-4172-4606
Lilje, P. B.0000-0003-4324-7794
Lloro, I.0000-0001-5966-1434
Maiorano, E.0000-0003-2593-4355
Mansutti, O.0000-0001-5758-4658
Marggraf, O.0000-0001-7242-3852
Marulli, F.0000-0002-8850-0303
Massey, R.0000-0002-6085-3780
Meneghetti, M.0000-0003-1225-7084
Moresco, M.0000-0002-7616-7136
Moscardini, L.0000-0002-3473-6716
Padilla, C.0000-0001-7951-0166
Paltani, S.0000-0002-8108-9179
Pettorino, V.0000-0002-4203-9320
Pires, S.0000-0002-0249-2104
Polenta, G.0000-0003-4067-9196
Raison, F.0000-0002-7819-6918
Renzi, A.0000-0001-9856-1970
Rhodes, J.0000-0002-4485-8549
Romelli, E.0000-0003-3069-9222
Saglia, R.0000-0003-0378-7032
Schneider, P.0000-0002-5094-2245
Schrabback, T.0000-0002-6987-7834
Secroun, A.0000-0003-0505-3710
Seidel, G.0000-0003-2907-353X
Tereno, I.0000-0002-4537-6218
Toledo-Moreo, R.0000-0002-2997-4859
Valentijn, E. A.0000-0003-1032-6680
Valenziano, L.0000-0002-1170-0104
Wang, Y.0000-0002-4749-2984
Weller, J.0000-0002-8282-2010
Zamorani, G.0000-0002-2318-301X
Andreon, S.0000-0002-2041-8784
Maino, D.0000-0002-4761-1242
de la Torre, S.0000-0002-0839-2884
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 (
Group:Infrared Processing and Analysis Center (IPAC)
Funding AgencyGrant Number
Academy of Finland292882
Academy of Finland295113
Agenzia Spaziale Italiana (ASI)UNSPECIFIED
Belgian Federal Science Policy Office (BELSPO)UNSPECIFIED
Canadian Euclid ConsortiumUNSPECIFIED
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
Deutsches Zentrum für Luft- und Raumfahrt (DLR)UNSPECIFIED
Danish Space Research InstituteUNSPECIFIED
Fundação para a Ciência e Tecnologia (FCT)UNSPECIFIED
Ministerio de Economía, Industria y Competitividad (MINECO)UNSPECIFIED
National Astronomical Observatory of JapanUNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Norwegian Space AgencyUNSPECIFIED
Romanian Space AgencyUNSPECIFIED
State Secretariat for Education, Research and Innovation (SERI)UNSPECIFIED
Swiss Space Office (SSO)UNSPECIFIED
United Kingdom Space Agency (UKSA)UNSPECIFIED
Record Number:CaltechAUTHORS:20221107-999291600.24
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117753
Deposited By: Research Services Depository
Deposited On:18 Nov 2022 21:39
Last Modified:19 Nov 2022 00:05

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