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The optical lightcurves of many quasars show variations of tenths of a magnitude or more on timescales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of over 20 deterministic and stochastic models on 6304 quasi-steller object (QSO) lightcurves in SDSS Stripe 82. We include the damped random walk (or Ornstein-Uhlenbeck [OU] process), a particular type of stochastic model, which recent studies have focused on. Further models we consider are single and double sinusoids, multiple OU processes, higher order continuous autoregressive processes, and composite models. We find that only 29 out of 6304 QSO lightcurves are described significantly better by a deterministic model than a stochastic one. The OU process is an adequate description of the vast majority of cases (6023). Indeed, the OU process is the best single model …