Date of Award
Doctor of Philosophy
Jarad B. Niemi
This work expounds a computationally expedient strategy for the fully Bayesian treatment of high-dimensional hierarchical models. Most steps in a Markov chain Monte Carlo routine for such models are either conditionally independent draws or low-dimensional draws based on summary statistics of parameters at higher levels of the hierarchy. We construct both sets of steps using parallelized algorithms designed to take advantage of the immense parallel computing power of general-purpose graphics processing units while avoiding the severe memory transfer bottleneck. We apply our strategy to RNA-sequencing (RNA-seq) data analysis, a multiple-testing, low-sample-size scenario where hierarchical models provide a way to borrow information across genes. Our approach is solidly tractable, and it performs well under several metrics of estimation, posterior inference, and gene detection. Best-case-scenario empirical Bayes counterparts perform equally well, lending support to existing empirical Bayes approaches in RNA-seq. Finally, we attempt to improve the robustness of estimation and inference of our RNA-seq model using alternate hierarchical distributions.
William Michael Landau
Landau, William Michael, "High-dimensional hierarchical models and massively parallel computing" (2016). Graduate Theses and Dissertations. 15745.