Date of Award

December 2020

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Member

Christopher McMahan

Committee Member

Andrew Brown

Committee Member

Sez Atamturktur

Committee Member

Yu-Bo Wang


This dissertation focuses on developing statistical models to analyze complex data. The motivating applications in this work include infectious disease screening, engineering, and public health problems. Chapters 2 and 3 take a frequentist approach to modeling and parameter estimation while Chapters 4 and 5 proceed with Bayesian methods. Maximum likelihood estimation is implemented in a case of missing data through latent variables (Chapter 2) as well as by embedding a finite element model within the likelihood framework (Chapter 3). Two Markov Chain Monte Carlo (MCMC) algorithms are applied to estimate parameters and fit regression models using data obtained from a coupled system (Chapter 4) and data depending on spatial random effects (Chapter 5). In particular, spike and slab prior distributions, Gibbs steps, and Metropolis-Hastings steps are used to complete estimation. The finite sample performance of our techniques are investigated using extensive numerical simulation studies that are based on the motivating data sets. The methods are then applied to data sets on the Heptatits B infection, spring and mass systems, acceleration data from vehicle-bridge coupled systems, and opioid overdoses in South Carolina.



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