Date of Award

December 2019

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Member

Christopher McMahan

Committee Member

Andrew Brown

Committee Member

Brook Russell

Committee Member

Xiaoqian Sun


This dissertation focuses on developing mixed effects models for large scale and complex data. Our motivating applications involve areas where this data is common, including epidemiological studies, environmental sciences, and genetics. Two key attributes for most of the modeling techniques discussed in this dissertation are that they scale easily to large data and that they achieve full variable selection, which is often a desirable trait in mixed effects models. These attributes are primarily handled in two ways. The first is with carefully constructed latent variables that we introduce to make the posterior distributions more tractable. This allows a Markov chain Monte Carlo (MCMC) sampler to be carried out with Gibbs steps, which results in efficient computation of posterior estimates, especially in large data scenarios. The second is through a decomposition of the covariance matrix associated with the random effects and with the use of spike and slab priors, we can achieve full variable selection in not only the fixed effects, but also the random effects. The finite sample performance of our techniques are assessed through extensive simulations and are used to analyze motivating data sets, which includes data from group testing procedures, human disease surveillance studies, and genetics.



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