The impact of signal-to-noise, redshift, and angular range on the bias of weak lensing 2-point functions

Abstract

Weak lensing data follow a naturally skewed distribution, implying the data vector most likely yielded from a survey will systematically fall below its mean. Although this effect is qualitatively known from CMB-analyses, correctly accounting for it in weak lensing is challenging, as a direct transfer of the CMB results is quantitatively incorrect. While a previous study (Sellentin et al. 2018) focused on the magnitude of this bias, we here focus on the frequency of this bias, its scaling with redshift, and its impact on the signal-to-noise of a survey. Filtering weak lensing data with COSEBIs, we show that weak lensing likelihoods are skewed up until ≈ 100, whereas CMB-likelihoods Gaussianize already at ≈ 20. While COSEBI-compressed data on KiDS-and DES-like redshift-and angular ranges follow Gaussian distributions, we detect skewness at 6σ significance for half of a Euclid-or LSST-like data set, caused by the wider coverage and deeper reach of these surveys. Computing the signal-to-noise ratio per data point, we show that precisely the data points of highest signal-to-noise are the most biased. Over all redshifts, this bias affects at least 10% of a survey's total signal-to-noise, at high redshifts up to 25%. The bias is accordingly expected to impact parameter inference. The bias can be handled by developing non-Gaussian likelihoods. Otherwise, it could be reduced by removing the data points of highest signal-to-noise.

KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics

“…A comparison of these figures shows that the probability distribution of ξ ± (θ) for the largest values of θ deviates from a Gaussian, while this is not the case for band powers and COSE-BIs. Louca & Sellentin (2020) also showed that the COSEBI likelihood is well approximated by a Gaussian for a survey such as KiDS. For our fiducial analysis we employ the angular ranges shown in Fig.…”

Dark energy survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

“…The DES 3x2pt analysis, described in Krause & Eifler et al, (2017), adopts a Gaussian likelihood for the 3x2pt data vector (see, e.g., Sellentin & Heavens 2018;Louca & Sellentin 2020, for a discussion of this approximation). The Gaussian likelihood, L, is determined by the expectation value of the data vector at parameters Θ, (Θ), and by a covariance matrix C,…”

Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

“…Since the dependence structure in a multivariate Gaussian distribution is also fully described by its covariance matrixsuch that the components of a multivariate Gaussian with diagonal covariance are independent -removing linear correlations removes all Gaussian dependence. This whitening follows the same process as Sellentin & Heavens (2018), , Diaz Rivero & Dvorkin (2020) and Louca & Sellentin (2020): each pair of data elements is whitened separately using a Cholesky whitening procedure followed by a mean subtraction. The result is a whitened pair having a mean of zero and a covariance matrix of the identity matrix.…”

“…Transcovariance is a measure of non-Gaussianity of a distribution introduced in Sellentin & Heavens (2018) and subsequently used in , Louca & Sellentin (2020) and Diaz Rivero & Dvorkin (2020). We will follow the latter three papers in considering only the additive transcovariance 𝑆 + , which is defined as…”

“…However, the true likelihood of weak lensing two-point statistics is well known to be non-Gaussian. This has been studied in detail in distributions of simulated data (Sellentin & Heavens 2018;Diaz Rivero & Dvorkin 2020;Louca & Sellentin 2020) and has motivated many derivations of non-Gaussian likelihoods, either approximate or exact under particular conditions (Taruya et al 2002;Sato et al 2010Sato et al , 2011Hilbert et al 2011;Keitel & Schneider 2011;Wilking & Schneider 2013;Sellentin 2015;Wilking et al 2015;Upham et al 2019;Manrique-Yus & Sellentin 2020;Diaz Rivero & Dvorkin 2020).…”