  High redshift quasars (HZQs) with redshifts of z >~ 6 are so rare that any
photometrically-selected sample of sources with HZQ-like colours is likely to
be dominated by Galactic stars and brown dwarfs scattered from the stellar
locus. It is impractical to reobserve all such candidates, so an alternative
approach was developed in which Bayesian model comparison techniques are used
to calculate the probability that a candidate is a HZQ, P_q, by combining
models of the quasar and star populations with the photometric measurements of
the object. This method was motivated specifically by the large number of HZQ
candidates identified by cross-matching the UKIRT Infrared Deep Sky Survey
(UKIDSS) Large Area Survey (LAS) to the Sloan Digital Sky Survey (SDSS): in the
~1900 deg^2 covered by the LAS in the UKIDSS Seventh Data Release (DR7) there
are ~10^3 real astronomical point-sources with the measured colours of the
target quasars, of which only ~10 are expected to be HZQs. Applying Bayesian
model comparison to the sample reveals that most sources with HZQ-like colours
have P_q <~ 0.1 and can be confidently rejected without the need for any
further observations. In the case of the UKIDSS DR7 LAS, there were just 88
candidates with P_q >= 0.1; these object were prioritized for reobservation by
ranking according to P_q (and their likely redshift, which was also inferred
from the photometric data). Most candidates were rejected after one or two
(moderate depth) photometric measurements by recalculating P_q using the new
data. That left seven confirmed HZQs, three of which were previously identified
in the SDSS and four of which were new UKIDSS discoveries. The high efficiency
of this Bayesian selection method suggests that it could usefully be extended
to other HZQ surveys (e.g. searches by Pan-STARRS or VISTA) as well as to other
searches for rare objects.
