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UBC Theses and Dissertations

A numerical study of the effects of the parameterization of the gaussian process Foster, Jodie Lynn


Mathematical models implemented as computer code are gaining widespread use across the sciences and engineering. In some cases these model are even replacing physical experiments. The computational complexity of the models typically limits the number of runs that can be performed. In such cases, the Gaussian process is used to emulate the true computer model so that experiments are performed on the emulator. The applicability of the emulator is closely related to the quality of the fitted Gaussian process model. A key step in fitting the Gaussian process is estimating the unknown correlation parameters using a numerical optimizer. It is well known that maximum likelihood estimation is invariant to the parameterization of the model. When the mapping from one parametrization to another is injective this leads to an equivalence of the likelihood and in a Bayesian context an equivalence of the posterior for carefully chosen prior distributions. In the context of a Gaussian process model, we show that the parameterization of the model is in fact critical to achieving meaningful results and ensuring convergence of the optimizer. This thesis is aimed at providing practical advice on the best parameterization for the Gaussian process model. The approach presented here implements a simulation study on a wide range of test problems and a large number of parameterizations. We illustrate that the parameterization can have a huge effect on the fitted model and show that many of the commonly used parameterizations are in fact sub-optimal for fitting the Gaussian process.

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