MOTIVATION: statistics from genome-wide association studies (GWAS) are widely used in fine-mapping and colocalization analyses to identify causal variants and their enrichment in functional contexts, such as affected cell types and genomic features. With the expansion of functional genomic (FG) datasets, which now include hundreds of thousands of tracks across various cell and tissue types, it is critical to establish scalable algorithms integrating thousands of diverse FG annotations with GWAS results. RESULTS: We propose BTS (Bayesian Tissue Score), a novel, highly efficient algorithm uniquely designed for (i) identifying affected cell types and functional elements (context-mapping) and (ii) fine-mapping potentially causal variants in a context-specific manner using large collections of cell type-specific FG annotation tracks. BTS leverages GWAS summary statistics and annotation-specific Bayesian models to analyze genome-wide annotation tracks, including enhancers, open chromatin, and histone marks. We evaluated BTS on GWAS summary statistics for immune and cardiovascular traits, such as Inflammatory Bowel Disease (IBD), Rheumatoid Arthritis (RA), Systemic Lupus Erythematosus (SLE), and Coronary Artery Disease (CAD). Our results demonstrate that BTS is over 100× more efficient in estimating functional annotation effects and context-specific variant fine-mapping compared to existing methods. Importantly, this large-scale Bayesian approach prioritizes both known and novel annotations, cell types, genomic regions, and variants and provides valuable biological insights into the functional contexts of these diseases. AVAILABILITY AND IMPLEMENTATION: Docker image is available at https://hub.docker.com/r/wanglab/bts with preinstalled BTS R package (https://bitbucket.org/wanglab-upenn/BTS-R) and BTS GWAS summary statistics analysis pipeline (https://bitbucket.org/wanglab-upenn/bts-pipeline).