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

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.; Silva, A. Da; 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.

doi:10.1051/0004-6361/202244065

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

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Blot, L.
MPI for Astrophysics, Max Planck Society;

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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., Silva, A. D., 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. (2022). Euclid: Fast two-point correlation function covariance through linear construction. Astronomy and Astrophysics, 666:. doi:10.1051/0004-6361/202244065.

引用: https://hdl.handle.net/21.11116/0000-000C-9047-1

要旨

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.