Efficient methods for Understanding the Genetic Architecture of Complex Traits

Understanding the genetic architecture of complex traits is a central goal of modern human genetics.Recent efforts focused on building large-scale biobanks, that collect genetic and trait data on large numbers of individuals, present exciting opportunities for understanding genetic architecture. However, these datasets also pose several statistical and computational challenges. In this dissertation, we consider a series of statistical models that allow us to infer aspects of the genetic architecture of single and multiple traits. Inference in these models is computationally challenging due to the size of the genetic data -- consisting of millions of genetic variants measured across hundreds of thousands of individuals.We propose a series of scalable computational methods that can perform efficient inference in these models and apply these methods to data from the UK Biobank to showcase their utility