The impact of spectroscopic incompleteness in direct calibration of
  redshift distributions for weak lensing surveys
  Obtaining accurate distributions of galaxy redshifts is a critical aspect of
weak lensing cosmology experiments. One of the methods used to estimate and
validate redshift distributions is apply weights to a spectroscopic sample so
that their weighted photometry distribution matches the target sample. In this
work we estimate the \textit{selection bias} in redshift that is introduced in
this procedure. We do so by simulating the process of assembling a
spectroscopic sample (including observer-assigned confidence flags) and
highlight the impacts of spectroscopic target selection and redshift failures.
We use the first year (Y1) weak lensing analysis in DES as an example data set
but the implications generalise to all similar weak lensing surveys. We find
that using colour cuts that are not available to the weak lensing galaxies can
introduce biases of $\Delta~z\sim0.015$ in the weighted mean redshift of
different redshift intervals. To assess the impact of incompleteness in
spectroscopic samples, we select only objects with high observer-defined
confidence flags and compare the weighted mean redshift with the true mean. We
find that the mean redshift of the DES Y1 weak lensing sample is typically
biased at the $\Delta~z=0.005-0.05$ level after the weighting is applied. The
bias we uncover can have either sign, depending on the samples and redshift
interval considered. For the highest redshift bin, the bias is larger than the
uncertainties in the other DES Y1 redshift calibration methods, justifying the
decision of not using this method for the redshift estimations. We discuss
several methods to mitigate this bias.
