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$\sigma$ 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.
