Single Nugget Kriging

TL;DR

This paper introduces a novel Kriging method that improves prediction accuracy at extreme values and demonstrates robustness to model mismatch and non-Gaussianity, especially useful for computer simulations with limited data.

Contribution

It presents a new Kriging predictor constructed by penalizing conditional bias and likelihood, enhancing robustness over standard methods.

Findings

Better predictions at extreme values.

Robustness to covariance parameter mismatch.

Effective on non-Gaussian functions.

Abstract

We propose a method with better predictions at extreme values than the standard method of Kriging. We construct our predictor in two ways: by penalizing the mean squared error through conditional bias and by penalizing the conditional likelihood at the target function value. Our prediction exhibits robustness to the model mismatch in the covariance parameters, a desirable feature for computer simulations with a restricted number of data points. Applications on several functions show that our predictor is robust to the non-Gaussianity of the function.