Propagating sample variance uncertainties in redshift calibration:
  simulations, theory and application to the COSMOS2015 data
  Cosmological analyses of galaxy surveys rely on knowledge of the redshift
distribution of their galaxy sample. This is usually derived from a
spectroscopic and/or many-band photometric calibrator survey of a small patch
of sky. The uncertainties in the redshift distribution of the calibrator sample
include a contribution from shot noise, or Poisson sampling errors, but, given
the small volume they probe, they are dominated by sample variance introduced
by large-scale structures. Redshift uncertainties have been shown to constitute
one of the leading contributions to systematic uncertainties in cosmological
inferences from weak lensing and galaxy clustering, and hence they must be
propagated through the analyses. In this work, we study the effects of sample
variance on small-area redshift surveys, from theory to simulations to the
COSMOS2015 data set. We present a three-step Dirichlet method of resampling a
given survey-based redshift calibration distribution to enable the propagation
of both shot noise and sample variance uncertainties. The method can
accommodate different levels of prior confidence on different redshift sources.
This method can be applied to any calibration sample with known redshifts and
phenotypes (i.e. cells in a self-organizing map, or some other way of
discretizing photometric space), and provides a simple way of propagating prior
redshift uncertainties into cosmological analyses. As a worked example, we
apply the full scheme to the COSMOS2015 data set, for which we also present a
new, principled SOM algorithm designed to handle noisy photometric data. We
make available a catalog of the resulting resamplings of the COSMOS2015
galaxies.
