Regularized radial basis function models for stochastic simulation

We propose a new radial basis function (RBF) model for stochastic simulation, called regularized RBF (R-RBF). We construct the R-RBF model by minimizing a regularized loss over a reproducing kernel Hilbert space (RKHS) associated with RBFs. The model can flexibly incorporate various types of RBFs including those with conditionally positive definite basis. To estimate the model prediction error, we first represent the RKHS as a stochastic process associated to the RBFs. We then show that the prediction model obtained from the stochastic process is equivalent to the R-RBF model and derive the associated mean squared error. We propose a new criterion for efficient parameter estimation based on the closed form of the leave-one-out cross validation error for R-RBF models. Numerical results show that R-RBF models are more robust, and yet fairly accurate compared to stochastic kriging models.