A Variational Inference-Based Heteroscedastic Gaussian Process Approach for Simulation Metamodeling

In this article, we propose a variational Bayesian inference-based Gaussian process metamodeling approach (VBGP) that is suitable for the design and analysis of stochastic simulation experiments. This approach enables statistically and computationally efficient approximations to the mean and variance response surfaces implied by a stochastic simulation, while taking into full account the uncertainty in the heteroscedastic variance; furthermore, it can accommodate the situation where either one or multiple simulation replications are available at every design point. We demonstrate the superior performance of VBGP compared with existing simulation metamodeling methods through two numerical examples.