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

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$σ$ 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.