Adaptive Design for Global Fit of Nonstationary Surfaces in Computer Experiments

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Marian Frazier*+ and William I. Notz
• Companies: Gustavus Adolphus College and Ohio State University
• Keywords: computer experiments ; Bayesian treed Gaussian processes ; sequential design

Abstract

Computer experiments are used to study processes that are too difficult or dangerous to experiment with in the physical world. Complex computer code that simulates these experiments often results in an extremely long run time. The design points at which to run the simulations must be chosen carefully and intelligently; thus, sequential designs that allow users to focus their attentions on interesting areas of the response are a logical choice. We propose a family of sequential design methods that are developed for use when it is believed that the response surface may exhibit non-stationary behavior. These criteria, which were inspired by an expected improvement criterion, focus on the search for areas with large changes in slope, with the idea that sudden changes in slope are an indication of non-stationary "breaks" in the response. While seeking out these boundary points, our methods still result in an effective fit of the entire response surface using a small number of design points. The merits of these methods are exhibited in a 2-dimensional example, including comparisons to existing sequential design methods.