Approximate Likelihood Methods for Estimation and Prediction in Gaussian Process Regression Models for Computer Experiments

• Activity Number: 539
• Type: Contributed
• Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Ryan Parker* and Brian J. Reich and Chris Gotwalt
• Companies: SAS Institute and North Carolina State University and SAS Institute
• Keywords: estimating equations ; sensitivity analysis ; optimization

Abstract

Computer model experiments are vital to understanding complex physical processes. A computer model uses deterministic equations to predict the response of the system to a potentially large number of inputs. These experiments are used to identify the optimal input values and to quantify the relevance of each input. These tasks require many model evaluations, which poses computational challenges for complex models. A common statistical approach is to fit a Gaussian Process (GP) regression model to these data, and then use the GP for fast prediction at a new set of inputs. Unfortunately, estimating the parameters in the GP model is challenging for large problems because the time required to evaluate the likelihood is cubic in the number of observations. In this paper we propose a simple method for estimating the GP parameters that scales linearly in the number of observations. Our approach is to split the observations into blocks and define an estimating equation that sums over these blocks. We show that this leads to huge computational improvements and that the predictions and sensitivity analysis from this approach are on par with those from the full likelihood estimates.