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.
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