Bayesian Analysis of Nonstationary Composite Gaussian Process Models

• Activity Number: 375
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Casey Davis*+ and Christopher Hans and Thomas Santner
• Companies: and Ohio State University and Ohio State University
• Keywords: Computer experiments ; Gaussian process ; non-stationarity ; prior distribution ; MCMC

Abstract

This research proposes a Bayesian formulation of the Composite Gaussian Process (GP) of Ba and Joseph (2012). The composite Gaussian Process model generalizes the regression plus stationary GP model for interpolating computationally expensive functions by replacing the regression term by a GP. This work shows how knowledge of the underlying function can be added to the model in the form of a prior distribution. We introduce alternate parameterizations of the model that simplify the specification and interpretation of the prior distribution. Markov chain Monte Carlo methods are used to estimate posterior predictive densities, and predictions from the Bayesian model are compared with predictions from the composite GP model.