Kriging in Multi-response Simulation, including a Monte Carlo Laboratory (Replaced by 2014-012)

Abstract: To analyze the input/output behavior of simulation models with multiple responses, we may apply either univariate or multivariate Kriging (Gaussian Process) models. Univariate Kriging may use a popular MATLAB Kriging toolbox called \DACE'. Multivariate Kriging faces a major problem: its covariance matrix should remain positive-definite; this problem may be solved through nonseparable dependence model. To evaluate the performance of these two Kriging models, we develop a Monte Carlo \laboratory' that simulates Gaussian Processes. To verify that this laboratory works correctly, we derive statistics that test whether the Kriging parameters have the correct values. Our Monte Carlo results demonstrate that in general DACE gives smaller Mean Squared Error (MSE); we also explain these results.