2004.04833
2D-FFTLog: efficient computation of real space covariance matrices for galaxy clustering and weak lensing
Fnag, Eifler, Krause
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. 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 DES Y3-like and an LSST Y1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances at the flat sky limit, which are sufficiently accurate for inferring cosmological parameters.
2D-FFTLog: efficient computation of real space covariance matrices for galaxy clustering and weak lensing
Fnag, Eifler, Krause
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. 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 DES Y3-like and an LSST Y1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances at the flat sky limit, which are sufficiently accurate for inferring cosmological parameters.
2004.05016
Can a conditioning on stellar mass explain the mutual information between morphology and environment?
Bhattacharjee, et al
Recent studies with SDSS have shown that a statistically significant non-zero mutual information between morphology and environment persists upto several tens of Mpc. It is important to understand the origin of these non-zero mutual information. Galaxies in different environments acquire their stellar mass through accretion and merger and the stellar mass function of galaxies is known to depend on both environment and morphology. Naturally, stellar mass can be an important link between morphology and environment which may explain the non-zero mutual information between the two. Measuring the mutual information between morphology and environment by conditioning the stellar mass would allow us to test this possibility. We compute the mutual information between morphology and environment by conditioning the stellar mass in a volume limited and stellar mass limited sample from SDSS DR16 and find a non-zero conditional mutual information throughout the entire length scales probed. The results suggest that only environmental and morphology dependence of stellar mass are inadequate in explaining the observed mutual information between morphology and environment. We compare the results with two semi analytic models implemented on the Millennium simulation. The predictions of the semi-analytic models are in fairly good agreement with the SDSS observations on smaller length scales but are noticeably smaller on larger length scales.
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