Statistical approaches for spatial prediction and anomaly detection

This dissertation is primarily a description of three projects. It starts with a method for spatial prediction and parameter estimation for irregularly spaced, and non-Gaussian data. It will be shown that by judiciously replacing the likelihood with an empirical likelihood in the Bayesian hierarchical model, approximate posterior distributions for the mean and covariance parameters can be obtained. Due to the complex nature of the hierarchical model, standard Markov chain Monte Carlo methods cannot be applied to sample from the posterior distributions. To overcome this issue, a generalized sequential Monte Carlo algorithm is used. Finally this method is applied to iron concentrations in California. The second project focuses on anomaly detection for functional data; specifically for func- tional data where the observed functions may lie over different domains. By approximating each function as a low-rank sum of spline basis functions the coefficients will be compared for each basis across each function. The idea being, if two functions are similar then their respective coefficients should not be significantly different. This project concludes with an application of the proposed method to detect anomalous behavior of users of a supercomputer at NREL. The final project is an extension of the second project to two-dimensional data. This project aims to detect location and temporal anomalies from ground motion data from a fiber-optic cable using distributed acoustic sensing (DAS). First, with a simulation study the validity of the proposed method is established. We present an application of the proposed method to detect the location of subsurface anomalies near the cable as well as temporal anomalies including an M3.6 earthquake.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Applied Mathematics and Statistics

Grantor dc:publisher

Colorado School of Mines. Arthur Lakes Library

Year dc:date.issued

2019

Author dc:creator

• Hannum, Caitlyn S.

Advisors dc:contributor.advisor

• Tenorio, Luis
• Bandyopadhyay, Soutir

Committee members dc:contributor.committeemember

• Nychka, Douglas
• Navidi, William Cyrus
• Trainor-Guitton, Whitney
• Bugbee, Bruce

• Bayesian statistics
• time-series
• spatial statistics
• anomaly detection

Statement dc:rights

• Copyright of the original work is retained by the author.

Language dc:language.iso

eng, English

Identifier

T 8715

OAI identifier oai:identifier

oai:repository.mines.edu:11124/173058