Learning Ancestral Genetic Processes using Nonparametric Bayesian Models

for the degree of Doctor of Philosophy. Recent explosion of genomic data have fueled the long-standing interest of analyzing genetic variations to reconstruct the evolutionary history and ancestral structures of human populations that can provide essential clues for various medical applications. Although genetic properties such as linkage disequilib-rium (LD) and population structure are closely related under a common inheritance process involving many different ancestral processes in the genetic history, the statistical methodologies developed so far mostly deal with those structural inferences separately using specialized models that do not capture their statistical and genetic relationships. Also, most of these approaches ignore the inherent uncertainty in the genetic complexity of the data and rely on inflexible models resulting from restrictive assumptions. These limitations may make it difficult to infer detailed and consistent structural information from rich genotypic data. The goal of this proposal is to develop new nonparametric Bayesian models for learning the ances-tral genetic processes under a unified inheritance framework. Our preliminary results include efficient models based on Dirichlet process for haplotype inference on multi-population data, and for the joint analysis of population structure and recombination events. We plan to generalize these models further to solve related problems in ancestral inference such as to recover local ancestries along chromosomes, or to detect the signatures of selective sweeps on the chromosomes. Rigorous statistical analysis will be performed as well as extensive validation on real large scaled data. The models would serve as valuable tools for downstream analysis such as to find genetic basis of phenotypic traits