Improving the accuracy of estimators for the two-point correlation function

Abstract

We show how to increase the accuracy of estimates of the two-point correlation function without sacrificing efficiency. We quantify the error of the pair-counts and of the Landy-Szalay estimator by comparing them with exact reference values. The standard method, using random point sets, is compared to geometrically motivated estimators and estimators using quasi-Monte~Carlo integration. In the standard method, the error scales proportionally to $1/\sqrt{N_r}$, with $N_r$ being the number of random points. In our improved methods, the error scales almost proportionally to $1/N_q$, where $N_q$ is the number of points from a low-discrepancy sequence. We study the run times of the new estimator in comparison to those of the standard estimator, keeping the same level of accuracy. For the considered case, we always see a speedup ranging from 50% up to a factor of several thousand. We also discuss how to apply these improved estimators to incompletely sampled galaxy catalogues.

15 pages, 10 figures, 3 tables, now includes a signifficantly extended discussion of run times and recommendations on the application, A&A accepted

References in corpus (6)

• Array Programming with NumPy
• Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1
• Corrfunc --- A Suite of Blazing Fast Correlation Functions on the CPU
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogs for Cosmological Analysis
• A Fast and Accurate Analytic Method of Calculating Galaxy Two-point Correlation Functions

Cited by in corpus (3)

• CSST Cosmological Emulator I: Matter Power Spectrum Emulation with one percent accuracy to k = 10 h/Mpc
• Pair Counting without Binning -- A New Approach to Correlation Functions in Clustering Statistics
• Angular correlation functions of bright Lyman-break galaxies at $3\lesssim \mathbf{z}\lesssim 5$