Diagnostics and Simulation-Based Methods for Validating Gaussian Process Emulators

Emulation is a statistical technique that can be utilised for estimating model simulations when the computer models are too computationally expensive to run. Emulators need to be subjected to a validation process since various assumptions have to be made. One assumption is that the computer model output is thought of as a realization of a Gaussian process with a mean and a covariance function. The computer model, however, is not a random sample from the Gaussian process distribution. In this thesis, we develop a graphical diagnostic that can be used to investigate whether the Gaussian process assumption is suitable for building emulators. Diagnostic methods can be used to assess the validity of the statistical model in order to investigate the best probability model for describing the computer model. However, it is not always possible to derive the required reference distribution for some diagnostics analytically. In this thesis, a simulation-based method is developed based on simulating samples from the posterior distribution of the output function. This simulation-based method can be used to obtain the reference distribution of diagnostics that cannot be obtained analytically. The observed diagnostic values will be `consistent' with the simulated diagnostic values if the Gaussian process emulator is valid.