A Class of Nonseparable and Nonstationary Covariance Functions for Multi-Ouput Gaussian Process

• Activity Number: 503 - SPAAC Poster Competition
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Scientific and Public Affairs Advisory Committee
• Author(s): Pulong Ma* and Bledar Alex Konomi and Emily L. Kang
• Companies: Department of Mathematical Sciences, University of Cincinnati and Department of Mathematical Sciences, University of Cincinnati and University of Cincinnati
• Keywords: Gaussian process emulator ; (modified) predictive process ; nonseparable and nonstationary covariance function ; Bayesian inference ; uncertainty quantification

Abstract

Gaussian process is widely used as a surrogate to emulate many computationally expensive simulators (computer models) in uncertainty quantification field due to its good theoretic properties and simplicity. The use of a separable covariance function in Gaussian process emulator is computationally convenient, which, however, ignores the interaction among input dimensions and performs very poor when quantifying uncertainties for computer model outputs. To allow efficient computation as well as quantify uncertainty correctly, we build a multi-output Gaussian process with its covariance function coming from two parts, one of which is constructed from (modified) predictive process, and the other of which has separable form with any covariance function for each input subspace. The resulting covariance function for the multi-output Gaussian process emulator is nonseparable, nonstationary, and allows efficient computation for very large datasets. Bayesian inference including parameter estimation and prediction are derived for the proposed multi-output Gaussian process emulator, and its performance is demonstrated with simulation examples and real data analysis.