Euclid: Fast two-point correlation function covariance through linear construction
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 (data-to-random 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 of size M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of these. We validate the method with PINOCCHIO simulations in range r = 20-200 Mpc/h, and show that the covariance estimate is unbiased. With M = 50 and with 2 Mpc/h bins, the theoretical speed-up of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and derive a formula for the covariance of covariance.
Cite
@article{arxiv.2205.11852,
title = {Euclid: Fast two-point correlation function covariance through linear construction},
author = {E. Keihanen and V. Lindholm and P. Monaco and L. Blot and C. Carbone and K. Kiiveri and A. G. Sánchez and A. Viitanen and J. Valiviita and A. Amara and N. Auricchio and M. Baldi and D. Bonino and E. Branchini and M. Brescia and J. Brinchmann and S. Camera and V. Capobianco and J. Carretero and M. Castellano and S. Cavuoti and A. Cimatti and R. Cledassou and G. Congedo and L. Conversi and Y. Copin and L. Corcione and M. Cropper and A. Da Silva and H. Degaudenzi and M. Douspis and F. Dubath and C. A. J. Duncan and X. Dupac and S. Dusini and A. Ealet and S. Farrens and S. Ferriol and M. Frailis and E. Franceschi and M. Fumana and B. Gillis and C. Giocoli and A. Grazian and F. Grupp and L. Guzzo and S. V. H. Haugan and H. Hoekstra and W. Holmes and F. Hormuth and K. Jahnke and M. Kümmel and S. Kermiche and A. Kiessling and T. Kitching and M. Kunz and H. Kurki-Suonio and S. Ligori and P. B. Lilje and I. Lloro and E. Maiorano and O. Mansutti and O. Marggraf and F. Marulli and R. Massey and M. Melchior and M. Meneghetti and G. Meylan and M. Moresco and B. Morin and L. Moscardini and E. Munari and S. M. Niemi and C. Padilla and S. Paltani and F. Pasian and K. Pedersen and V. Pettorino and S. Pires and G. Polenta and M. Poncet and L. Popa and F. Raison and A. Renzi and J. Rhodes and E. Romelli and R. Saglia and B. Sartoris and P. Schneider and T. Schrabback and A. Secroun and G. Seidel and C. Sirignano and G. Sirri and L. Stanco and C. Surace and P. Tallada-Crespí and D. Tavagnacco and A. N. Taylor and I. Tereno and R. Toledo-Moreo and F. Torradeflot and E. A. Valentijn and L. Valenziano and T. Vassallo and Y. Wang and J. Weller and G. Zamorani and J. Zoubian and S. Andreon and D. Maino and S. de la Torre},
journal= {arXiv preprint arXiv:2205.11852},
year = {2022}
}
Comments
17 pages, 11 figures