  Established techniques for simulation and prediction with Gaussian process
(GP) dynamics often implicitly make use of an independence assumption on
successive function evaluations of the dynamics model. This can result in
significant error and underestimation of the prediction uncertainty,
potentially leading to failures in safety-critical applications. This paper
discusses methods that explicitly take the correlation of successive function
evaluations into account. We first describe two sampling-based techniques; one
approach provides samples of the true trajectory distribution, suitable for
`ground truth' simulations, while the other draws function samples from basis
function approximations of the GP. Second, we propose a linearization-based
technique that directly provides approximations of the trajectory distribution,
taking correlations explicitly into account. We demonstrate the procedures in
simple numerical examples, contrasting the results with established methods.

Machine Learning;Systems and Control;Systems and Control;Machine Learning