  Gaussian processes that can be decomposed into a smooth mean function and a
stationary autocorrelated noise process are considered and a fully automatic
nonparametric method to simultaneous estimation of mean and auto-covariance
functions of such processes is developed. Our empirical Bayes approach is
data-driven, numerically efficient and allows for the construction of
confidence sets for the mean function. Performance is demonstrated in
simulations and real data analysis. The method is implemented in the R package
eBsc that accompanies the paper.
