  We develop a method for separating quasars from other variable point sources
using SDSS Stripe 82 light curve data for ~10,000 variable objects. To
statistically describe quasar variability, we use a damped random walk model
parametrized by a damping time scale, tau, and an asymptotic amplitude
(structure function), SF_inf. With the aid of an SDSS spectroscopically
confirmed quasar sample, we demonstrate that variability selection in typical
extragalactic fields with low stellar density can deliver complete samples with
reasonable purity (or efficiency, E). Compared to a selection method based
solely on the slope of the structure function, the inclusion of the tau
information boosts E from 60% to 75% while maintaining a highly complete sample
(98%) even in the absence of color information. For a completeness of C=90%, E
is boosted from 80% to 85%. Conversely, C improves from 90% to 97% while
maintaining E=80% when imposing a lower limit on tau. With the aid of color
selection, the purity can be further boosted to 96%, with C= 93%. Hence,
selection methods based on variability will play an important role in the
selection of quasars with data provided by upcoming large sky surveys, such as
Pan-STARRS and the Large Synoptic Survey Telescope (LSST). For a typical
(simulated) LSST cadence over 10 years and a photometric accuracy of 0.03 mag
(achieved at i~22), C is expected to be 88% for a simple sample selection
criterion of tau>100 days. In summary, given an adequate survey cadence,
photometric variability provides an even better method than color selection for
separating quasars from stars.
