A General Covariance Structure of Gaussian Processes Model with Quantitative and Qualitative Inputs

• Activity Number: 77
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Yulei Zhang*+ and William I. Notz
• Companies: and Ohio State University
• Keywords: Gaussian Processes Model ; Quantitative and Qualitative Inputs ; Kronecker Product ; ANOVA Decomposition ; Linear Decomposition

Abstract

The framework for building Gaussian stochastic processes(GaSP) model with quantitative and qualitative inputs was first proposed by Qian et al.(2008). The idea is to construct the correlation function with quantitative and qualitative inputs. Based on the cross-correlation between different qualitative levels, we can borrow the information from all the observations. However, the difference between some qualitative levels may exist not only in smoothness, but also in variance. Illustrated by examples, the cross-correlation structure may fail to capture the true relationship between different levels in these cases. Inspired by multivariate analysis, we built a more general construction of the covariance function by converting GaSP with several qualitative levels into a linear combination of independent stochastic processes with fewer constraints on the variance and correlation functions. Furthermore, the general covariance structure can be extended into the case with multiple qualitative inputs. In these cases, we introduced the Kronecker product form of the covariance function, which can not only reduce the number of the parameters, but also capture the similarity between differen