Prior distributions for Gaussian processes in computer model emulation and calibration

This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance parameter, and correlation parameters. These parameters are often estimated by maximum likelihood (MLE). In some scenarios, however, the MLE can be unstable, particularly when the number of simulation runs is small, and some Bayesian estimators display better properties. We introduce default Bayesian priors for the parameters of GPs with isotropic and separable correlation functions for emulating computer simulations with both scalar-valued and vector-valued outputs. We also summarize recent developments of Bayesian priors for calibrating computer models by field or experimental observations. Finally, we review software packages for computer model emulation and calibration.