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 2h(-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.

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

M. Baldi;A. Cimatti;F. Marulli;M. Moresco;L. Moscardini;E. Munari;
2022

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 2h(-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.
2022
E. Keih??nen; V. Lindholm; P. Monaco; L. Blot; C. Carbone; K. Kiiveri; A. G. S??nchez; A. Viitanen; J. Valiviita; A. Amara; N. Auricchio; M. Baldi; D. Bonino; E. Branchini; M. Brescia; J. Brinchmann; S. Camera; V. Capobianco; J. Carretero; M. Castellano; S. Cavuoti; A. Cimatti; R. Cledassou; G. Congedo; L. Conversi; Y. Copin; L. Corcione; M. Cropper; A. Da Silva; H. Degaudenzi; M. Douspis; F. Dubath; C. A. J. Duncan; X. Dupac; S. Dusini; A. Ealet; S. Farrens; S. Ferriol; M. Frailis; E. Franceschi; M. Fumana; B. Gillis; C. Giocoli; A. Grazian; F. Grupp; L. Guzzo; S. V. H. Haugan; H. Hoekstra; W. Holmes; F. Hormuth; K. Jahnke; M. K??mmel; S. Kermiche; A. Kiessling; T. Kitching; M. Kunz; H. Kurki-Suonio; S. Ligori; P. B. Lilje; I. Lloro; E. Maiorano; O. Mansutti; O. Marggraf; F. Marulli; R. Massey; M. Melchior; M. Meneghetti; G. Meylan; M. Moresco; B. Morin; L. Moscardini; E. Munari; S. M. Niemi; C. Padilla; S. Paltani; F. Pasian; K. Pedersen; V. Pettorino; S. Pires; G. Polenta; M. Poncet; L. Popa; F. Raison; A. Renzi; J. Rhodes; E. Romelli; R. Saglia; B. Sartoris; P. Schneider; T. Schrabback; A. Secroun; G. Seidel; C. Sirignano; G. Sirri; L. Stanco; C. Surace; P. Tallada-Cresp??; D. Tavagnacco; A. N. Taylor; I. Tereno; R. Toledo-Moreo; F. Torradeflot; E. A. Valentijn; L. Valenziano; T. Vassallo; Y. Wang; J. Weller; G. Zamorani; J. Zoubian; S. Andreon; D. Maino; S. de la Torre
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/905063
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