Statistical Methods for Genomic Data Analysis

Advances in genomics technology have produced a wealth of data, offering new insights into complex biological processes. However, interpreting these large datasets requires statistical methods capable of handling high dimensionality and low signal-to-noise ratios. This dissertation addresses problems in unsupervised learning of large data matrices such as those seen in genomics by building on ideas from Bayesian statistics and random matrix theory. We first present B-SMaRT, a Bayesian multinomial mixture model with a multi-stage MCMC algorithm designed to identify sites that have changed in frequency over time in response to treatment. Simulation studies show that while B-SMaRT achieves accuracy comparable to other model-based clustering approaches, it produces results in just a fraction of the time. When applied to time-sampled influenza A H1N1 populations exposed to oseltamivir (Tamiflu), B-SMaRT correctly identifies the known H275Y resistance mutation and reveals additional sites that show evidence of adaptation due to culture conditions. The second part of this dissertation addresses signal recovery from noisy matrices when the noise level is unknown. Using ideas from random matrix theory, we propose a trimmed median estimator (TriME) that improves signal recovery over existing methods in challenging rank and signal strength regimes. Applying these findings to the Data Integration via Analysis of Subspaces (DIVAS) framework, we show that poor noise level estimates can distort the decomposition of shared and individual structure. Finally, we apply DIVAS with TriME to a multi-assay tuberculosis study to identify common and distinct modes of variation between bulk and pseudobulked single-cell RNA-sequencing data.