Flexible Correlation Structure for Accurate Prediction and Uncertainty Quantification in Bayesian Gaussian Process Emulation of a Computer Model
Hao Chen, Jason L. Loeppky, William J. Welch · SIAM/ASA Journal on Uncertainty Quantification · 2017
Gaussian processes are widely used in the analysis of data from a computer model. Ideally, the analysis will yield accurate predictions with correct coverage probabilities of credible intervals. In this paper, we first review several existing Bayesian implementations in the literature. We show that Bayesian approaches with squared-exponential correlation structure do not always quantify well the uncertainty in prediction. Thus, we propose new Bayesian approaches with power-exponential or Matérn correlation structure, which have more flexibility. Through application examples and a simulation study, we show that the proposed Bayesian methods not only have superior prediction accuracy but are closer to having the correct coverage probability.