Project Summary The overall goal of this project is to develop new statistical methods that address important problems in ge- nomics, to implement them in user-friendly open source software, and to make them available to scientists to facilitate new biological discoveries. To this end, the proposed work tackles three important problems arising in genomics where existing statistical methods are lacking, and where new, improved methods could accelerate the pace of scientific discovery: fine-mapping of functional traits; gene set enrichment analysis (GSEA); and discovering overlapping cluster structure in genomic data. The work on fine-mapping will enable the identification of genetic variants influencing common sequencing assays such as ATAC-seq and ChIP-seq, without pre-specifying the locations of potential effects. This unbiased approach will help identify regulatory genetic variants and interacting parts of the regulatory genome. The work on GSEA will provide a new more effective set of tools for researchers who use GSEA to set new findings in the context of known biology. The proposed work uses recently-developed statistical techniques to substantially reduce the redundancy of enriched gene sets, and will provide researchers with succinct and precise results that better highlight the full range of known biological factors that are relevant to a new set of findings. The work on overlapping cluster structure will provide new generally-applicable methods for understanding complex layered and hierarchical relationships that occur commonly in genomics applications (e.g. cell sub- types nested within cell types, layered on top of patient effects). The tools developed here will help scientists tackle a diverse range of analysis problems that arise in ge- nomics, ultimately helping them better understand the biology of disease, with the eventual goal of improving therapies and treatment strategies.