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

TL;DR

This paper investigates how signal-to-noise ratio, redshift, and angular range influence the bias in weak lensing 2-point functions, revealing significant skewness in data distributions and proposing methods to mitigate bias for accurate cosmological inference.

Contribution

It provides a detailed analysis of the frequency, scaling, and impact of bias in weak lensing data, highlighting the importance of non-Gaussian likelihoods and data filtering techniques.

Findings

Likelihood skewness persists up to high multipoles for weak lensing.

High signal-to-noise data points are most biased.

Bias affects at least 10% of the total signal-to-noise, up to 25% at high redshifts.

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 $\ell \approx 100$, whereas CMB-likelihoods Gaussianize already at $\ell \approx 20$. While COSEBI-compressed data on KiDS- and DES-like redshift- and angular ranges follow Gaussian distributions, we detect skewness at 6$\sigma$ 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.