Statistical Methods For Spatial And Multivariate Spatial Extreme Values
Open Access
- Author:
- Nascimento, Mauricio
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 19, 2020
- Committee Members:
- Benjamin A. Shaby, Dissertation Advisor/Co-Advisor
Benjamin A. Shaby, Committee Chair/Co-Chair
Ephraim Mont Hanks, Committee Member
Lynn Lin, Committee Member
Chris Eliot Forest, Outside Member
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- Extreme Values
Dirichlet Mixture
Angular Distribution
Scale Mixture - Abstract:
- Chapter 1: We analyze the joint tail of two variables related to fire threat associated with SantaAna Winds in Southern California. To do this, we apply a flexible model for the joint tail of asymptotically dependent multivariate distributions, when samples are taken at several locations across space. We use a spatial prior on the underlying multivariate extremal dependence structure, which enables us to borrow strength across space while still allowing for different joint tail distributions at different spatial locations, and to predict the joint tail of the distribution at un-observed locations. A simulation shows that this model is able to capture complex dependence structures well. Chapter 2: We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to implement using standard software. We demonstrate its accuracy and computational efficiency in a series of simulation experiments, and apply it to analyzing the joint tail of a large precipitation dataset using a recently-proposed scale mixture model for spatial extremes. This dataset is many times larger than what was previously considered possible to fit using preferred inferential techniques. Chapter 3: We analyze the remaining lifetime of simulated engines from the NASA Commercial MModular Aero-Propulsion System Simulation. We apply a variety of regression methods, including models with change point detection, to accommodate features of the data. We demonstrate the accuracy of this method using MSE and compare it with competing methods from previous published papers. We conclude that the changepoint model has better results than some of the previous works and that performance increases when looking at smaller values of remaining lifetime.