Design on Nonconvex Regions: Optimal Experiments for Spatial Process Prediction with Applications to Industrial Processes

• Activity Number: 282
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Matthew Pratola*+
• Companies: Simon Fraser University
• Keywords: optimal design ; non-convex ; spatial ; Gaussian ; process ; ISOMAP

Abstract

Modeling a response over a non-convex design region is a common problem in many areas of industrial research, such as engineering and geophysics. Unfortunately, the tools available to model and design for such responses are limited as standard methods are not appropriate. Some success has been found by applying the Gaussian Process (GP) model with a non-Euclidean distance metric. A difficulty is that transformation of this metric is required to be able to model a GP over such regions. The questions of how to make this transformation, select design points and fit GP models have received little attention. Our work builds on existing results to propose a valid transformation. A new method for selecting design points with the GP model over non-convex regions is proposed. Optimal designs for prediction are described, and a simulation study demonstrates the improvements that are realized.