A Dual Metamodeling Perspective for Design and Analysis of Stochastic Simulation Experiments

Fueled by a growing number of applications in science and engineering, the development of stochastic simulation metamodeling methodologies has gained momentum in recent years. A majority of the existing methods, such as stochastic kriging (SK), only focus on efficiently metamodeling the mean response surface implied by a stochastic simulation experiment. As the simulation outputs are stochastic with the simulation variance varying significantly across the design space, suitable methods for variance modeling are required. This thesis takes a dual metamodeling perspective and aims at exploiting the benefits of fitting the mean and variance functions simultaneously for achieving an improved predictive performance. We first explore the effects of replacing the sample variances with various smoothed variance estimates on the performance of SK and propose a dual metamodeling approach to obtain an efficient simulation budget allocation rule. Second, we articulate the links between SK and least-square support vector regression and propose to use a dense and shallow'' initial design to facilitate selection of important design points and efficient allocation of the computational budget. Third, we propose a variational Bayesian inference-based Gaussian process (VBGP) metamodeling approach to accommodate the situation where either one or multiple simulation replications are available at every design point. VBGP can fit the mean and variance response surfaces simultaneously, while taking into full account the uncertainty in the heteroscedastic variance. Lastly, we generalize VBGP for handling large-scale heteroscedastic datasets based on the idea of transductive combination of GP experts.''