Recent advances in computer experiment modeling

OF THE DISSERTATION Recent Advances in Computer Experiment Modeling by YUFAN LIU Dissertation Director: Ying Hung This dissertation develops methodologies for analysis of computer experiments and its related theories. Computer experiments are becoming increasingly important in science and Gaussian process (GP) models are widely used in the analysis of computer experiments. This dissertation focuses on two settings where massive data are observed on irregular grids or quantiles of correlated data are of interests. In this dissertation, we first develop Latin Hypercube Design-based Block Bootstrap method. Then, we investigate quantiles of computer experiments in which correlated data are observed and propose penalized quantile regression with asymmetric Laplace process. The computational issue that hinders GP from broader application is recognized, especially for massive data observed on irregular grids. To overcome the computational issue, we introduce an efficient framework based on a novel experimental design based bootstrap method. The main challenge in GP modeling is the estimation of maximum likelihood estimators because it relies heavily on large correlation matrix operations, which are computationally intensive and often intractable for massive data. Using the