Photometric Redshift Probability Distributions for Galaxies in the SDSS
  DR8
  We present redshift probability distributions for galaxies in the SDSS DR8
imaging data. We used the nearest-neighbor weighting algorithm presented in
Lima et al. 2008 and Cunha et al. 2009 to derive the ensemble redshift
distribution N(z), and individual redshift probability distributions P(z) for
galaxies with r < 21.8. As part of this technique, we calculated weights for a
set of training galaxies with known redshifts such that their density
distribution in five dimensional color-magnitude space was proportional to that
of the photometry-only sample, producing a nearly fair sample in that space. We
then estimated the ensemble N(z) of the photometric sample by constructing a
weighted histogram of the training set redshifts. We derived P(z) s for
individual objects using the same technique, but limiting to training set
objects from the local color-magnitude space around each photometric object.
Using the P(z) for each galaxy, rather than an ensemble N(z), can reduce the
statistical error in measurements that depend on the redshifts of individual
galaxies. The spectroscopic training sample is substantially larger than that
used for the DR7 release, and the newly added PRIMUS catalog is now the most
important training set used in this analysis by a wide margin. We expect the
primary source of error in the N(z) reconstruction is sample variance: the
training sets are drawn from relatively small volumes of space. Using
simulations we estimated the uncertainty in N(z) at a given redshift is 10-15%.
The uncertainty on calculations incorporating N(z) or P(z) depends on how they
are used; we discuss the case of weak lensing measurements. The P(z) catalog is
publicly available from the SDSS website.
