Hierarchical Bayesian inference of galaxy redshift distributions from
  photometric surveys
  Accurately characterizing the redshift distributions of galaxies is essential
for analysing deep photometric surveys and testing cosmological models. We
present a technique to simultaneously infer redshift distributions and
individual redshifts from photometric galaxy catalogues. Our model constructs a
piecewise constant representation (effectively a histogram) of the distribution
of galaxy types and redshifts, the parameters of which are efficiently inferred
from noisy photometric flux measurements. This approach can be seen as a
generalization of template-fitting photometric redshift methods and relies on a
library of spectral templates to relate the photometric fluxes of individual
galaxies to their redshifts. We illustrate this technique on simulated galaxy
survey data, and demonstrate that it delivers correct posterior distributions
on the underlying type and redshift distributions, as well as on the individual
types and redshifts of galaxies. We show that even with uninformative priors,
large photometric errors and parameter degeneracies, the redshift and type
distributions can be recovered robustly thanks to the hierarchical nature of
the model, which is not possible with common photometric redshift estimation
techniques. As a result, redshift uncertainties can be fully propagated in
cosmological analyses for the first time, fulfilling an essential requirement
for the current and future generations of surveys.
