Multivariate versus univariate Kriging metamodels for multi-response simulation models

To analyze the input/output behavior of simulation models with multiple responses, we may apply either univariate or multivariate Kriging (Gaussian process) metamodels. In multivariate Kriging we face a major problem: the covariance matrix of all responses should remain positive-definite; we therefore use the recently proposed “nonseparable dependence” model. To evaluate the performance of univariate and multivariate Kriging, we perform several Monte Carlo experiments that simulate Gaussian processes. These Monte Carlo results suggest that the simpler univariate Kriging gives smaller mean square error.