Bootstrapping and Conditional Simulation in Kriging: Better Confidence Intervals and Optimization (Replaced by CentER DP 2014-076)

Abstract: This paper investigates two related questions: (1) How to derive a confidence interval for the output of a combination of simulation inputs not yet simulated? (2) How to select the next combination to be simulated when searching for the optimal combination? To answer these questions, the paper uses parametric bootstrapped Kriging and "conditional simulation". Classic Kriging estimates the variance of its predictor by plugging-in the estimated GP parameters so this variance is biased. The main conclusion is that classic Kriging seems quite robust; i.e., classic Kriging gives acceptable confidence intervals and estimates of the optimal solution