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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.; [...]

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

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  • Media type: E-Article
  • Title: Euclid: Fast two-point correlation function covariance through linear construction
  • Contributor: 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.; [...]
  • imprint: EDP Sciences, 2022
  • Published in: Astronomy & Astrophysics
  • Language: Not determined
  • DOI: 10.1051/0004-6361/202244065
  • ISSN: 0004-6361; 1432-0746
  • Keywords: Space and Planetary Science ; Astronomy and Astrophysics
  • Origination:
  • Footnote:
  • Description: <jats:p>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 <jats:italic>M</jats:italic> ≫ 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 <jats:italic>M</jats:italic> = 1 and <jats:italic>M</jats:italic> = 2, and the covariance for arbitrary <jats:italic>M</jats:italic> 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 <jats:italic>r</jats:italic> = 20 − 200 <jats:italic>h</jats:italic><jats:sup>−1</jats:sup> Mpc. With <jats:italic>M</jats:italic> = 50 and with 2 <jats:italic>h</jats:italic><jats:sup>−1</jats:sup> 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.</jats:p>
  • Access State: Open Access