  The Model-free Prediction Principle has been successfully applied to general
regression problems, as well as problems involving stationary and locally
stationary time series. In this paper we demonstrate how Model-Free Prediction
can be applied to handle random fields that are only locally stationary, i.e.,
they can be assumed to be stationary only across a limited part over their
entire region of definition. We construct one-step-ahead point predictors and
compare the performance of Model-free to Model-based prediction using models
that incorporate a trend and/or heteroscedasticity. Both aspects of the paper,
Model-free and Model-based, are novel in the context of random fields that are
locally (but not globally) stationary. We demonstrate the application of our
Model-based and Model-free point prediction methods to synthetic data as well
as images from the CIFAR-10 dataset and in the latter case show that our best
Model-free point prediction results outperform those obtained using Model-based
prediction.
