Design on Non-Convex Regions: Optimal Experiments for Spatial Process Prediction

Matthew Pratola successfully defended his M.Sc. project entitled "Design on Non-Convex Regions: Optimal Experiments for Spatial Process Prediction" on 2 August 2006.

Scientists frequently perform experiments on physical systems to help understand how a response is affected by adjusting the levels of certain factors. In many setups, the levels of some factors are not independent of one another. As a result, the corresponding design region for the factors is non-rectangular. If the design space remains convex, modeling can proceed in the normal fashion. However, this is not the case when the design space is non-convex.

Modeling the behavior of a system that is a function of a non-convex design region is a common problem in diverse areas such as engineering and geophysics. Although this issue occurs frequently, the tools available to properly model and design for such responses are limited. It turns out that response surface analyses (e.g., linear regression) are inappropriate in the case of non-convex design regions.

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 trans- formation 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 de- sign points and fit GP models have received little attention. In this thesis, 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.

This type of interdisciplinary work is a hallmark of our program in Applied Statistics at Simon Fraser University. For more information, please contact Matthew Pratola (mtpratol@irmacs.ca) or his supervisor Derek Bingham (dbingham@stat.sfu.ca), Department of Statistics and Actuarial Science.

2 August 2006