Euclid preparation: X. The Euclid photometric-redshift challenge
  Forthcoming large photometric surveys for cosmology require precise and
accurate photometric redshift (photo-z) measurements for the success of their
main science objectives. However, to date, no method has been able to produce
photo-$z$s at the required accuracy using only the broad-band photometry that
those surveys will provide. An assessment of the strengths and weaknesses of
current methods is a crucial step in the eventual development of an approach to
meet this challenge. We report on the performance of 13 photometric redshift
code single value redshift estimates and redshift probability distributions
(PDZs) on a common set of data, focusing particularly on the 0.2--2.6 redshift
range that the Euclid mission will probe. We design a challenge using emulated
Euclid data drawn from three photometric surveys of the COSMOS field. The data
are divided into two samples: one calibration sample for which photometry and
redshifts are provided to the participants; and the validation sample,
containing only the photometry, to ensure a blinded test of the methods.
Participants were invited to provide a redshift single value estimate and a PDZ
for each source in the validation sample, along with a rejection flag that
indicates sources they consider unfit for use in cosmological analyses. The
performance of each method is assessed through a set of informative metrics,
using cross-matched spectroscopic and highly-accurate photometric redshifts as
the ground truth. We show that the rejection criteria set by participants are
efficient in removing strong outliers, sources for which the photo-z deviates
by more than 0.15(1+z) from the spectroscopic-redshift (spec-z). We also show
that, while all methods are able to provide reliable single value estimates,
several machine-learning methods do not manage to produce useful PDZs.
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