A Sequential Split-Conquer-Combine Approach for Gaussian Process Modeling in Computer Experiments

• Activity Number: 384 - Bayes, Frequentist, Fiducial: BFF in Action
• Type: Invited
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Ying Hung* and Minge Xie and Chengrui Li
• Companies: and Rutgers University and Rutgers University
• Keywords: Computer experiments ; Confidence distribution ; Gaussian process model ; Uncertainty quantification

Abstract

Gaussian process (GP) models are widely used in the analysis of computer experiments. However, two critical issues remain unresolved. One is the computational issue in GP estimation and prediction and the other is how to improve the naive plug-in predictive distribution which is known to underestimate the uncertainty. In this article, we introduce an unified framework that can tackle both issues simultaneously. It consists of a sequential split-conquer (SSC) procedure, an information combining technique using confidence distributions (CDs), and a CD-based predictive distribution. This framework provides an estimate and a predictor that dramatically reduces the computation and achieves the same asymptotic efficiency as the conventional method. It is also shown that the CD-based predictive distribution provides better quantification of the prediction uncertainty compared with the plug-in predictive distribution. Simulations are conducted to evaluate the finite sample performance. The proposed method is illustrated by a data center example based on tens of thousands of computer experiments generated from a computational fluid dynamic simulator.