Dark Energy Survey Year 3 results: Marginalisation over redshift
  distribution uncertainties using ranking of discrete realisations
  Cosmological information from weak lensing surveys is maximised by dividing
source galaxies into tomographic sub-samples for which the redshift
distributions are estimated. Uncertainties on these redshift distributions must
be correctly propagated into the cosmological results. We present hyperrank, a
new method for marginalising over redshift distribution uncertainties in
cosmological analyses, using discrete samples from the space of all possible
redshift distributions. This is demonstrated in contrast to previous highly
simplified parametric models of the redshift distribution uncertainty. In
hyperrank the set of proposed redshift distributions is ranked according to a
small (in this work between one and four) number of summary values, which are
then sampled along with other nuisance parameters and cosmological parameters
in the Monte Carlo chain used for inference. This can be regarded as a general
method for marginalising over discrete realisations of data vector variation
with nuisance parameters, which can consequently be sampled separately to the
main parameters of interest, allowing for increased computational efficiency.
We focus on the case of weak lensing cosmic shear analyses and demonstrate our
method using simulations made for the Dark Energy Survey (DES). We show the
method can correctly and efficiently marginalise over a range of models for the
redshift distribution uncertainty. Finally, we compare hyperrank to the common
mean-shifting method of marginalising over redshift uncertainty, validating
that this simpler model is sufficient for use in the DES Year 3 cosmology
results presented in companion papers.
