Department of Astronomy and Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85719, USA
Department of Astronomy and Steward Observatory, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85719, USA, Department of Physics, University of Arizona, 1118 E. Fourth Street, Tucson, AZ 85721, USA
Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.
Fang, et al. "2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing." Monthly Notices of the Royal Astronomical Society, vol. 497, no. 3, Jun. 2020. https://doi.org/10.1093/mnras/staa1726
Fang, Eifler, Tim, & Krause, Elisabeth (2020). 2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing. Monthly Notices of the Royal Astronomical Society, 497(3). https://doi.org/10.1093/mnras/staa1726
Fang, Eifler, Tim, and Krause, Elisabeth, "2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing," Monthly Notices of the Royal Astronomical Society 497, no. 3 (2020), https://doi.org/10.1093/mnras/staa1726
@article{osti_1647116,
author = {Fang and Eifler, Tim and Krause, Elisabeth},
title = {2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing},
annote = {ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.},
doi = {10.1093/mnras/staa1726},
url = {https://www.osti.gov/biblio/1647116},
journal = {Monthly Notices of the Royal Astronomical Society},
issn = {ISSN 0035-8711},
number = {3},
volume = {497},
place = {United Kingdom},
publisher = {Oxford University Press},
year = {2020},
month = {06}}
National Aeronautics and Space Administration (NASA); USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0020215; SC0020247
OSTI ID:
1647116
Alternate ID(s):
OSTI ID: 1656795
Journal Information:
Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 3 Vol. 497; ISSN 0035-8711