A method for the updating of stochastic kriging metamodels

Abstract

Two standard approaches to predicting the expected values of simulation outputs are either execution of the simulation itself or the use of a metamodel. In this work we propose a methodology that enables both approaches to be combined. When a prediction for a new input is required the procedure is to augment the metamodel forecast with additional simulation outputs for a given input. The key benefit of the method is that it is possible to reach the desired prediction accuracy at a new input faster than in the case when no initial metamodel is present. We show that such a procedure is computationally simple and can be applied to, for instance, web-based simulations, where response time to user actions is often crucial.In this analysis we focus on stochastic kriging metamodels. We show that if this type of metamodel is used and we assume that its metaparameters are fixed, then updating such a metamodel with new observations is equivalent to a Bayesian forecast combination under the known variance assumption. Additionally we observe that using metamodel predictions of variance instead of point estimates for estimation of stochastic kriging metamodes can lead to improved metamodel performance.