Seal, Souvik2020-10-262020-10-262020-08https://hdl.handle.net/11299/216834University of Minnesota Ph.D. dissertation. August 2020. Major: Biostatistics. Advisors: Saonli Basu, Cavan Reilly. 1 computer file (PDF); xi, 128 pages.Recent developments in genotyping technologies have opened up many new possibilities of unraveling the genetic basis of common diseases. The past decade has seen an advent of a bunch of large scale cohort studies giving us, the researchers, access to an unprecedented wealth of data providing information on millions of genetic variants and numerous diseases/traits on millions of individuals. But, efficient analysis of such high-dimensional data demands non-traditional yet novel statistical techniques. The development of a complex human disease is an intricate interplay of genetic and environmental factors. In order to better understand such traits, we are often interested in estimating the overall trait heritability: the proportion of total trait variance due to genetic factors within a given population. Accurate estimation and inference of heritability give us some basic understanding of disease risk and etiology. Traits with high estimated heritability incite interest among the researchers for a further Genome-Wide Association Study (GWAS) to pinpoint significant genetic variants. As we move into the era of genome editing and personalized medicine, addressing the shared genetic basis of multiple diseases/traits or the genetic basis of a single disease/trait over multiple time-points becomes more and more important. In light of these exciting statistical problems, my thesis focuses on developing robust tools for estimating heritability and performing GWAS in large scale cohort studies both in a univariate and multivariate context.enThesis or Dissertation