Computer Experiments with Both Qualitative and Quantitative Inputs

• Activity Number: 103
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): William Notz*+ and Gang Han and Thomas J. Santner
• Companies: The Ohio State University and Moffitt Cancer Center & Research Institute and The Ohio State University
• Keywords: computer experiments ; qualitative inputs ; ANOVA-decomposition

Abstract

Gaussian Stochastic Process models are a popular way to model output from computer experiments. Unfortunately, the correlation functions typically used in these models assume inputs are quantitative. We propose a method for handling both quantitative and qualitative inputs. First, we consider an ANOVA-type decomposition of the output (as a function of the inputs) into an overall mean trend, first order departures from this mean trend, and higher order departures. Second, to model these trends we use a Bayesian approach with a prior on the correlation parameters that assumes they are draws from some common distribution. We demonstrate that our method works very well when there is a common underlying shape to the response for each value of the qualitative variables. Our method is also shown to compare favorably with other methods that have been recently proposed.