Statistical Models for Large Scale Genomic Data

Abstract

Sequencing technologies transformed how scientists examine biological systems at both macroscopic and microscopic level. For example, population-scale genome sequencing has cataloged millions of common and rare genetic variants in humans and enabled genotype imputation; new spatial transcriptomics technologies can resolve the sequences and locations of individual transcripts in tissues at submicron resolution. The massive amount of data generated by these technologies poses new scientific questions and challenges. This dissertation proposes statistical models and methods motivated by observations in large-scale sequencing data.

In Chapter 2, we study genotype imputation accuracy through the lens of the coalescent. We focus on rare variants where imputation is most challenging and investigate the theoretical upper bound of their imputation accuracy under the reference-based genotype imputation framework. We develop closed-form solutions for the probability distribution of the joint genealogy of the target and reference sequences, quantify the inevitable error rate of imputation, and evaluate the error’s impact on association studies across a range of allele frequencies and reference sample sizes.

In Chapter 3, we infer population level germline methylation using only the allele frequencies from public genetic variant catalogs. We observe that the high mutation rates at methylated CpGs distort the site frequency spectrum and leave a distinct signature in genomic regions hyper-methylated in germline. Leveraging this observation, we build a Hidden Markov Model that generates a unique resource for CpG methylation status in human germline cells and overcomes limitations in whole genome bisulfite sequencing measurements.

In Chapter 4, we develop a factor analysis method for sub-micron resolution spatial transcriptomics. We achieve segmentation-free sub-cellular resolution inference and scale our analysis to data with hundreds of millions of spatial locations. We apply our method to data from four platforms including both spatial barcoding and sequencing based technologies and textit{in situ} imaging-based technologies. Our method delineates cell type boundaries precisely and identifies rare cell populations even in complex tissue regions where cell segmentation fails.