Kriging metamodel with modified nugget-effect: The heteroscedastic variance case

Metamodels are commonly used to approximate and analyze simulation models. However, in cases where the simulation output variances are non-zero and not constant, many of the current metamodels which assume homogeneity, fail to provide satisfactory estimation. In this paper, we present a kriging model with modified nugget-effect adapted for simulations with heterogeneous variances. The new model improves the estimations of the sensitivity parameters by explicitly accounting for location dependent non-constant variances and smoothes the kriging predictor’s output accordingly. We look into the effects of stochastic noise on the parameter estimation for the classic kriging model that assumes deterministic outputs and note that the stochastic noise increases the variability of the classic parameter estimation. The nugget-effect and proposed modified nugget-effect stabilize the estimated parameters and decrease the erratic behavior of the predictor by penalizing the likelihood function affected by stochastic noise. Several numerical examples suggest that the kriging model with modified nugget-effect outperforms the kriging model with nugget-effect and the classic kriging model in heteroscedastic cases.

► Modified nugget-effect kriging model is proposed for general stochastic simulations.
► Stochastic noise affects parameter estimation in classic kriging models.
► Modified nugget-effect stabilizes estimated parameters and reduces erratic behaviour.
► Modified nugget-effect model outperforms classic kriging models in numerical examples.