Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


School of Mathematical and Statistical Sciences

Committee Chair/Advisor

Christopher McMahan

Committee Member

Joe Bible

Committee Member

Deborah Kunkel

Committee Member

Xinyi Li


This dissertation proposes three novel Bayesian modeling techniques to addresses the challenges arising from the complex, underlying features of biomedical data. These models are motivated by three different biomedical studies. The first is an analysis of data collected from six efficacy and safety clinical trials of buprenorphine maintenance treatment for opioid use disorder. The focus of this study is to overcome the problem of non-adherence by trial participants that, if left unaccounted for, obscures the true effect of buprenorphine on illicit opioid use. The second study is the assessment of hemodialysis cannulation skill through the use of a sensor-based simulator that provides objective metrics quantifying various facets of cannulation skill. The main objective of this study is to identify salient features from a high-dimensional feature space that influence multiple cannulation outcomes that are highly correlated, both implicitly and by design, while also addressing the presence of multicollinearity within the feature space. The third and final study focuses on modeling an individual’s probability of disease from data collected on pooled specimens. The primary barrier of this study is measurement error: the individual disease statuses are likely to be obscured by the group testing protocol and the testing responses (on pools and individuals) are subject to misclassification due to imperfect testing. The key objective of this study is to develop a flexible model that can account for imperfect testing and can be used to analyze data arising from any group testing protocol. A key attribute of the proposed modeling techniques is that they scale easily to extremely large data sets. The scalability of the modeling strategies discussed here is accomplished by introducing carefully constructed latent random variables to develop Markov chain Monte Carlo (MCMC) sampling algorithms that consist primarily of Gibbs steps. This results in efficient computation of posterior estimates, especially in large data scenarios.



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