Large-scale genome-wide association studies (GWAS) have produced a rich resource of genetic data over the past decade, urging the need to develop computational and statistical methods that analyze these data. This dissertation presents four statistical methods that model the correlation structure between genetic variants and its effect on GWAS summary association statistics to help understand the genetic basis of complex human traits and diseases.

The first method employs the multivariate Bernoulli distribution to model haplotype data, allowing for higher-order interactions among genetic variants, and shows better accuracy in predicting DNase I hypersensitivity status.

The second method partitions heritability into small regions on the genome using GWAS summary statistics data, while accounting for complex correlation structures among genetic variants, and uncovers the genetic architectures of complex human traits and diseases.

Extending the second method into pairs of traits, the third method partitions genetic correlation into small genomic regions using GWAS summary statistics data, and provides insights into the shared genetic basis between pairs of traits.

Finally, the fourth method dissects population-specific and shared causal genetic variants of complex traits in two continental populations, using GWAS summary statistics data obtained from samples of different ethnicities, and reveals differences in genetic architectures of two continental populations.