Standard techniques in optimal design of experiments (aka active learning) are based on independent errors and therefore observations. When the random errors are correlated, we require to consider some nonstandard techniques. In physical experiments, this situation
mainly happens when investigating the optimal allocation of sensors (monitoring stations)and observations in different sites are spatially correlated, but it is also common in computer simulation experiments. Here we concentrate our interest on model discrimination when there exists more than one potential explanatory model. Our main goal is thus to discriminate between (two) different Gaussian Processes (GPs). For these considered error processes
we assume to know the underlying respective covariance kernels, although we subsequently may need to estimate their unknown parameters. For simplicity the mean functions will be assumed to be known.We consider a number of different modes of design construction for model discrimination.
The first strategy is an incremental design strategy for which points are added conditionally on previous design points. When the observations associated with the already collected points are available, one may base the criterion on the predictions and prediction errors.