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

October 2022 • 2022A&A...666A.129K

Authors • Keihänen, 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. • 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, C. A. J. • Dupac, X. • Dusini, S. • Ealet, A. • Farrens, S. • Ferriol, S. • Frailis, M. • Franceschi, E. • Fumana, M. • Gillis, B. • Giocoli, C. • Grazian, A. • Grupp, F. • Guzzo, L. • Haugan, S. V. H. • Hoekstra, H. • Holmes, W. • Hormuth, F. • Jahnke, K. • Kümmel, M. • Kermiche, S. • Kiessling, A. • Kitching, T. • Kunz, M. • Kurki-Suonio, H. • Ligori, S. • Lilje, P. B. • Lloro, I. • Maiorano, E. • Mansutti, O. • Marggraf, O. • Marulli, F. • Massey, R. • Melchior, M. • Meneghetti, M. • Meylan, G. • Moresco, M. • Morin, B. • Moscardini, L. • Munari, E. • Niemi, S. M. • Padilla, C. • Paltani, S. • Pasian, F. • Pedersen, K. • Pettorino, V. • Pires, S. • Polenta, G. • Poncet, M. • Popa, L. • Raison, F. • Renzi, A. • Rhodes, J. • Romelli, E. • Saglia, R. • Sartoris, B. • Schneider, P. • Schrabback, T. • Secroun, A. • Seidel, G. • Sirignano, C. • Sirri, G. • Stanco, L. • Surace, C. • Tallada-Crespí, P. • Tavagnacco, D. • Taylor, A. N. • Tereno, I. • Toledo-Moreo, R. • Torradeflot, F. • Valentijn, E. A. • Valenziano, L. • Vassallo, T. • Wang, Y. • Weller, J. • Zamorani, G. • Zoubian, J. • Andreon, S. • Maino, D. • de la Torre, S.

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.

This paper is published on behalf of the Euclid Consortium.

Links

• POSTSCRIPT https://www.aanda.org/10.1051/0004-6361/202244065/postscript
• PDF https://www.aanda.org/10.1051/0004-6361/202244065/pdf
• PREPRINT http://arxiv.org/abs/2205.11852
• ELECTR https://doi.org/10.1051%2F0004-6361%2F202244065