Classic Kriging versus Kriging with bootstrapping or conditional simulation: classic Kriging’s robust confidence intervals and optimization

Abstract

Kriging is a popular method for estimating the global optimum of a simulated system. Kriging approximates the input/output function of the simulation model. Kriging also estimates the variances of the predictions of outputs for input combinations not yet simulated. These predictions and their variances are used by ‘efficient global optimization’ (EGO), to balance local and global search. This article focuses on two related questions: (1) How to select the next combination to be simulated when searching for the global optimum? (2) How to derive confidence intervals for outputs of input combinations not yet simulated? Classic Kriging simply plugs the estimated Kriging parameters into the formula for the predictor variance, so theoretically this variance is biased. This article concludes that practitioners may ignore this bias, because classic Kriging gives acceptable confidence intervals and estimates of the optimal input combination. This conclusion is based on bootstrapping and conditional simulation.

Keywords:

• simulation
• optimization
• Kriging
• bootstrap
• conditional simulation

Acknowledgements

We thank Inneke van Nieuwenhuyse (K.U. Leuven, Leuven, Belgium) for sharing her MATLAB code for EGO using BK and her help with the implementation of that code, Dick den Hertog (Tilburg University) for suggesting the investigation of dimensionality effects on the variance, and three anonymous reviewers for their very useful comments on a previous version.