Reduced-dimensional Non-Gaussian Spatial Models and Statistical Methods for Studying the West Antarctic Ice Sheet
Open Access
Author:
Guan, Yawen
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 20, 2017
Committee Members:
Murali Haran, Dissertation Advisor/Co-Advisor Murali Haran, Committee Chair/Co-Chair Francesca Chiaromonte, Committee Member Ephraim Mont Hanks, Committee Member Chris Eliot Forest, Outside Member
Keywords:
Spatial Model Non-Gaussian Spatial Data Markov chain Monte Carlo Expectation Maximization West Antarctic Ice Sheet Glacier Dynamics Bayesian Hierarchical Model Gaussian Process Latent Gaussian Process Model
Abstract:
My dissertation research focuses on developing efficient statistical methods for high-dimensional non-Gaussian spatial data, and hierarchical models for the West Antarctic Ice Sheet (WAIS). My thesis consists of three projects: (1) A fast projection-based approach to model high-dimensional non-Gaussian data on a continuous spatial domain. This involves developing a novel low-dimensional reparameterization of a spatial generalized linear mixed model (SGLMM). (2) A fast maximum likelihood inferential approach for high-dimensional non-Gaussian spatial data. This involves developing an automated Markov chain Monte Carlo Expectation Maximization algorithms for two reparameterized SGLMMs, one for discrete-domain Gaussian Markov random field models, and the other for continuous-domain Gaussian process spatial models. (3) A rigorous method for inferring important characteristics of the WAIS by combining multiple data sources while respecting physical constraints. Therefore, modeling and computational approaches for high-dimensional non-Gaussian spatial data are the underlying theme for all three projects.
