<i>Euclid</i>: Fast two-point correlation function covariance through linear construction

Journal article

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.Peer reviewe

Authors: Keihänen, E; Lindholm, V; Monaco, P; Blot, L; Carbone, C

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: EDP Sciences
• Journal: Astronomy & Astrophysics
• Volume: 666
• Pages: A129-A129
• Publication date: 2022-08-11
• Acceptance date: 2022-06-27
• DOI: 10.1051/0004-6361/202244065
• EISSN: 1432-0746
• ISSN: 0004-6361
• Language: English
• Keywords: Correlation function (quantum field theory); Law of total covariance; Spectral density; Random variable; Mathematics; Statistics; Function (biology); Sum of normally distributed random variables; Matérn covariance function; Applied mathematics; Estimator; Covariance intersection; Multivariate random variable; Algorithm; Covariance function; Physics; Rational quadratic covariance function; Covariance matrix; Estimation of covariance matrices; Covariance and correlation; Covariance; Covariance mapping