  We analyze a sample of optical light curves for 100 quasars, 70 of which have
black hole mass estimates. Our sample is the largest and broadest used yet for
modeling quasar variability. The sources in our sample have z < 2.8 and 10^6 <
M_BH < 10^10. We model the light curves as a continuous time stochastic
process, providing a natural means of estimating the characteristic time scale
and amplitude of quasar variations. We employ a Bayesian approach to estimate
the characteristic time scale and amplitude of flux variations; our approach is
not affected by biases introduced from discrete sampling effects. We find that
the characteristic time scales strongly correlate with black hole mass and
luminosity, and are consistent with disk orbital or thermal time scales. In
addition, the amplitude of short time scale variations is significantly
anti-correlated with black hole mass and luminosity. We interpret the optical
flux fluctuations as resulting from thermal fluctuations that are driven by an
underlying stochastic process, such as a turbulent magnetic field. In addition,
the intranight variations in optical flux implied by our empirical model are <
0.02 mag, consistent with current microvariability observations of radio-quiet
quasars. Our stochastic model is therefore able to unify both long and short
time scale optical variations in radio-quiet quasars as resulting from the same
underlying process, while radio-loud quasars have an additional variability
component that operates on time scales < 1 day.
