Abstract: Gaussian process (GP) models are widely used in the analysis of computer experiments. However, two issues have not been solved satisfactorily. The first is a computational issue that prevents GP models from being more widely applied, especially for massive data with high-dimensional inputs. The second is the underestimation of the prediction uncertainty in GP modeling. To tackle these problems simultaneously, we propose two methods for constructing GP predictive distributions based on a new version of bootstrap subsampling. The new subsampling procedure borrows the strength of space-filling designs to provide an efficient subsample, and thus reduce the computational complexity. Compared with the plug-in approach, this procedure provides unbiased predictors and offers an efficient analogue of conventional bootstrap predictive distributions with empirical coverage probabilities closer to their nominal levels. We illustrate the proposed methods using two complex computer experiments with high-dimensional inputs and tens of thousands of simulation outputs.

Key words and phrases: Computer experiment, experimental design, kriging, space-filling design, sub-bagging, uncertainty quantification.