Validating Gaussian Process Models in Computer Experiments

In this thesis we present a methodology for validating Gaussian process models: Gaussian process emulators and simulator discrepancy models. A Gaussian process emulator is a representation of our beliefs about a mathematical model implemented in a computer program known as a simulator. By ``simulator discrepancy'', we mean the difference between a simulator's output and the corresponding physical process. We present a set of diagnostics to validate and assess the adequacy of Gaussian process models. These diagnostics are based on comparisons between real observations and model predictions for some test data, known as validation data, defined by a sample of real observations not used to build the model. The validation data are chosen according to designs that we have developed for such purposes. The diagnostics for Gaussian process emulators and discrepancy models are useful tools during the modelling procedure. Based on the result of the diagnostics, we can identify problems such as underconfidence, overconfidence, poor estimation of some unknown parameters, which if not identified might compromise analyses using the Gaussian process models. After we identify a problem, the diagnostics may provide information on where we should collect more data in order to make the predictive model a better representation of our beliefs.