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Recent advances in computer experiments: prediction accuracy of kriging and a new framework of calibration

Thursday, February 8, 2018 - 16:00 to 17:00
Rui Tuo, Georgia Institute of Technology
Statistics Seminar
Room 4192, Earth Sciences Building (2207 Main Mall)

This talk will focus on two problems in computer experiments: 1) error estimates for kriging prediction; 2) a new framework for calibration of computer models.

Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work we obtain some error bounds for the (simple) kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers cases where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions.

The goal of calibration is to identify the model parameters in deterministic computer experiments, which cannot be measured or are not available in physical experiments. In a study of the prevailing Bayesian method proposed by Kennedy and O’Hagan (2001), Tuo-Wu (2015, 2016) and Tuo-Wang-Wu (2017) find that this method may render unreasonable estimation for the calibration parameters. Two novel methods are proposed and proven to enjoy nice properties. In an application example, we study a calibration problem for a composite fuselage simulation. The calibration of computer model parameters is conducted with the help of engineering design knowledge. An effective method is proposed to identify and adjust the important calibration parameters with limited physical experimental data.