  Being observed only one billion years after the Big Bang, z ~ 7 quasars are a
unique opportunity for exploring the early Universe. However, only two z ~ 7
quasars have been discovered in near-infrared surveys: the quasars ULAS
J1120+0641 and ULAS J1342+0928 at z = 7.09 and z = 7.54, respectively. The
Canada-France High-z Quasar Survey in the Near Infrared (CFHQSIR) has been
carried out to search for z ~ 7 quasars using near-infrared and optical imaging
from the Canada-France Hawaii Telescope (CFHT). Our data consist of $\rm{\sim
130\,deg^{2}}$ of Wide-field Infrared Camera (WIRCam) Y-band images up to a
5{\sigma} limit of $\rm{Y_{AB}}$ ~ 22.4 distributed over the
Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Wide fields. After
follow-up observations in J band, a first photometric selection based on simple
colour criteria led us to identify 36 sources with measured high-redshift
quasar colours. However, we expect to detect only ~ 2 quasars in the redshift
range 6.8 < z < 7.5 down to a rest-frame absolute magnitude of $\rm{M_{1450}}$
= -24.6. With the motivation of ranking our high-redshift quasar candidates in
the best possible way, we developed an advanced classification method based on
Bayesian formalism in which we model the high-redshift quasars and low-mass
star populations. The model includes the colour diversity of the two
populations and the variation in space density of the low-mass stars with
Galactic latitude, and it is combined with our observational data. For each
candidate, we compute the probability of being a high-redshift quasar rather
than a low-mass star. This results in a refined list of the most promising
candidates. Our Bayesian selection procedure has proven to be a powerful
technique for identifying the best candidates of any photometrically selected
sample of objects, and it is easily extendable to other surveys.
