Design on non-convex regions: Optimal experiments for spatial process prediction

Modeling a response over a non-convex design region is a common problem in diverse areas such as engineering and geophysics. Unfortunately, the tools available to model and design for such responses are limited. Recently, some success has been found by applying the Gaussian Process (GP) model with the so-called water distance metric. However, a difficulty is that transformation of the water distances is required to be able to model a GP over such regions. The specific questions of exactly how to make this transformation, select design points and fit GP models have received little attention. In this thesi s, we build on existing results to propose a valid transformation. A new method for selecting design points with the GP model over non-convex regions is then proposed. Optimal designs for prediction are described, and a simulation study is used to demonstrate the improvements that are realized.