  We define a copula process which describes the dependencies between
arbitrarily many random variables independently of their marginal
distributions. As an example, we develop a stochastic volatility model,
Gaussian Copula Process Volatility (GCPV), to predict the latent standard
deviations of a sequence of random variables. To make predictions we use
Bayesian inference, with the Laplace approximation, and with Markov chain Monte
Carlo as an alternative. We find both methods comparable. We also find our
model can outperform GARCH on simulated and financial data. And unlike GARCH,
GCPV can easily handle missing data, incorporate covariates other than time,
and model a rich class of covariance structures.
