Euclid: Fast two-point correlation function covariance through linear construction
Creators: name: Keihanen, E.
name: Lindholm, V.
name: Monaco, P.
name: Blot, L.
name: Carbone, C.
name: Kiiveri, K.
name: Sánchez, A. G.
name: Viitanen, A.
name: Valiviita, J.
name: Amara, A.
name: Auricchio, N.
name: Baldi, M.
name: Bonino, D.
name: Branchini, E.
name: Brescia, M.
name: Brinchmann, J.
name: Camera, S.
name: Capobianco, V.
name: Carretero, J.
name: Castellano, M.
name: Cavuoti, S.
name: Cimatti, A.
name: Cledassou, R.
name: Congedo, G.
name: Conversi, L.
name: Copin, Y.
name: Corcione, L.
name: Cropper, M.
name: Da Silva, A.
name: Degaudenzi, H.
name: Douspis, M.
name: Dubath, F.
name: Duncan, C. A. J.
name: Dupac, X.
name: Dusini, S.
name: Ealet, A.
name: Farrens, S.
name: Ferriol, S.
name: Frailis, M.
name: Franceschi, E.
name: Fumana, M.
name: Gillis, B.
name: Giocoli, C.
name: Grazian, A.
name: Grupp, F.
name: Guzzo, L.
name: Haugan, S. V. H.
name: Hoekstra, H.
name: Holmes, W.
name: Hormuth, F.
name: Jahnke, K.
name: Kümmel, M.
name: Kermiche, S.
name: Kiessling, A.
name: Kitching, T.
name: Kunz, M.
name: Kurki-Suonio, H.
name: Ligori, S.
name: Lilje, P. B.
name: Lloro, I.
name: Maiorano, E.
name: Mansutti, O.
name: Marggraf, O.
name: Marulli, F.
name: Massey, R.
name: Melchior, M.
name: Meneghetti, M.
name: Meylan, G.
name: Moresco, M.
name: Morin, B.
name: Moscardini, L.
name: Munari, E.
name: Niemi, S. M.
name: Padilla, C.
name: Paltani, S.
name: Pasian, F.
name: Pedersen, K.
name: Pettorino, V.
name: Pires, S.
name: Polenta, G.
name: Poncet, M.
name: Popa, L.
name: Raison, F.
name: Renzi, A.
name: Rhodes, J.
name: Romelli, E.
name: Saglia, R.
name: Sartoris, B.
name: Schneider, P.
name: Schrabback, T.
name: Secroun, A.
name: Seidel, G.
name: Sirignano, C.
name: Sirri, G.
name: Stanco, L.
name: Surace, C.
name: Tallada-Crespí, P.
name: Tavagnacco, D.
name: Taylor, A. N.
name: Tereno, I.
name: Toledo-Moreo, R.
name: Torradeflot, F.
name: Valentijn, E. A.
name: Valenziano, L.
name: Vassallo, T.
name: Wang, Y.
name: Weller, J.
name: Zamorani, G.
name: Zoubian, J.
name: Andreon, S.
name: Maino, D.
name: de la Torre, S.
Publisher: name: arXiv
Year: 2022
Subjects: subject: Cosmology and Nongalactic Astrophysics (astro-ph.CO)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: 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 (data-to-random objects ratio M&gt;&gt;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 of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.
description: 17 pages, 11 figures