Design and analysis of computer experiments for stochastic systems

Abstract

This thesis studies the design and analysis of computer experiment for stochastic simulations. The stochastic simulation models play an important role in modern industrial and managerial applications. However, its stochastic response increases the difficulties of conducting analysis and experiments. This thesis proposes the kriging metamodel with modified nugget effect as a solution to the more general stochastic simulation scenario with hetergeneous variances. The results suggest that the proposed model performs beter than the existing models by appropriately account for the influence of random noise in terms of model prediction and parameter estimation. The study on parameter estimation uncertainty problem with kriging metamodels in stochastic simulation is further investigated. Based on the proposed model, a two-stage optimization algorithm is also developed as the solution to stochastic simulation optimization for heteroscedastic case. The numerical results suggest that the proposed model can effective reduce the erratic behavior of the predictor by more appropriately accounting for the influence of the stochastic responses. Last, a Bayesian metamodeling and two-stage sequential design approach are also developed to overcome the parameter estimation uncertainty issue and efficiently use the limited computing budget in practice.