Bayesian Treed Gaussian Process Models With an Application to Computer Modeling

• Published in: Journal of the American Statistical Association Vol. 103; no. 483; pp. 1119 - 1130
• Main Authors: Gramacy, Robert B, Lee, Herbert K. H
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.09.2008; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Applications and Case Studies; Bayesian method; Booster rocket engines; Computer based modeling; Computer modeling; Computer simulator; Correlations; Covariance; Datasets; Exact sciences and technology; Experimental design; Experiments; General topics; Heteroscedasticity; Linear models; Mathematical functions; Mathematics; Model testing; Modeling; NASA; Nonparametric regression; Nonstationary spatial model; Outer space; Probability and statistics; Probability theory and stochastic processes; Recursive partitioning; Sciences and techniques of general use; Sideslip; Simulation; Simulations; Simulators; Spatial analysis; Spatial models; Statistical analysis; Statistical methods; Statistics; Stochastic processes; Studies; Bayes estimation; Recursive partitioning; Nonparametric regression; Computing; Heteroscedasticity; Statistical method; Nonstationary spatial model; Computer simulator; Gaussian process; Experimental design; Gaussian processes; Stationary process; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214508000000689

Motivated by a computer experiment for the design of a rocket booster, this article explores nonstationary modeling methodologies that couple stationary Gaussian processes with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. The methodological developments and statistical computing details that make this approach efficient are described in detail. In addition to providing an analysis of the rocket booster simulator, we show that our approach is effective in other arenas as well.