Stochastic Order Redshift Technique (SORT): a simple, efficient and
  robust method to improve cosmological redshift measurements
  We present a simple, efficient and robust approach to improve cosmological
redshift measurements. The method is based on the presence of a reference
sample for which a precise redshift number distribution (dN/dz) can be obtained
for different pencil-beam-like sub-volumes within the original survey. For each
sub-volume we then impose: (i) that the redshift number distribution of the
uncertain redshift measurements matches the reference dN/dz corrected by their
selection functions; and (ii) the rank order in redshift of the original
ensemble of uncertain measurements is preserved. The latter step is motivated
by the fact that random variables drawn from Gaussian probability density
functions (PDFs) of different means and arbitrarily large standard deviations
satisfy stochastic ordering. We then repeat this simple algorithm for multiple
arbitrary pencil-beam-like overlapping sub-volumes; in this manner, each
uncertain measurement has multiple (non-independent) "recovered" redshifts
which can be used to estimate a new redshift PDF. We refer to this method as
the Stochastic Order Redshift Technique (SORT). We have used a state-of-the-art
N-body simulation to test the performance of SORT under simple assumptions and
found that it can improve the quality of cosmological redshifts in an efficient
and robust manner. Particularly, SORT redshifts are able to recover the
distinctive features of the 'cosmic web' and can provide unbiased measurement
of the two-point correlation function on scales > 4 Mpc/h. Given its
simplicity, we envision that a method like SORT can be incorporated into more
sophisticated algorithms aimed to exploit the full potential of large
extragalactic photometric surveys.
