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theses

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 idea of design-based data reduction, the proposed framework provides an asymptotically consistent estimation for the parameters in GP with a dramatic reduction in computation. The finite-sample performance is examined through simulation studies. We illustrate the proposed method by a data center example based on tens of thousands of computer experiments generated from a computational fluid dynamics simulator. GP models and many other existing approaches focus on modeling the conditional mean of the response variable in computer experiments. Little work has been done to study quantile regression model that incorporate data dependence although in practice it is often of substantial interest. In addition, high dimensional data often display heterogeneity and call for models with sparsity in which only a small number of covariates have influence on the conditional distribution of the response. We propose a new modeling framework to model different quantiles in computer experiments and identify important effects for each quantile. The proposed approach utilize asymmetric Laplace process (ALP) instead of Gaussian process modeling. Also, penalized likelihood estimators for ALP are studied. We show that penalized quantile asymmetric Laplace estimator can select true relevant covariates when the number of covariates is large and the number of covariates is able to grow to infinity with the number of observations increasing infinity. Penalized quantile regression with asymmetric Laplace process is demonstrated numerically with simulation and a real data example.

ETD_5388

Ph.D.

Includes bibliographical references

by Yufan Liu

doi:10.7282/T38G8J1H

ETD doctoral

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