We present the SDSS-XDQSO quasar targeting catalog for efficient flux-based
quasar target selection down to the faint limit of the Sloan Digital Sky Survey
(SDSS) catalog, even at medium redshifts (2.5 <~ z <~ 3) where the stellar
contamination is significant. We build models of the distributions of stars and
quasars in flux space down to the flux limit by applying the
extreme-deconvolution method to estimate the underlying density. We convolve
this density with the flux uncertainties when evaluating the probability that
an object is a quasar. This approach results in a targeting algorithm that is
more principled, more efficient, and faster than other similar methods. We
apply the algorithm to derive low-redshift (z < 2.2), medium-redshift (2.2 <= z
3.5) quasar probabilities for all 160,904,060
point sources with dereddened i-band magnitude between 17.75 and 22.45 mag in
the 14,555 deg^2 of imaging from SDSS Data Release 8. The catalog can be used
to define a uniformly selected and efficient low- or medium-redshift quasar
survey, such as that needed for the SDSS-III's Baryon Oscillation Spectroscopic
Survey project. We show that the XDQSO technique performs as well as the
current best photometric quasar-selection technique at low redshift, and
outperforms all other flux-based methods for selecting the medium-redshift
quasars of our primary interest. We make code to reproduce the XDQSO quasar
target selection publicly available
