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Fine-mapping is commonly used to identify putative causal variants at genome-wide significant loci. Here we propose a Bayesian model for fine-mapping that has several advantages over existing methods, including flexible specification of the prior distribution of effect sizes, joint modeling of summary statistics and functional annotations and accounting for discrepancies between summary statistics and external linkage disequilibrium in meta-analyses. Using simulations, we compare performance with commonly used fine-mapping methods and show that the proposed model has higher power and lower false discovery rate (FDR) when including functional annotations, and higher power, lower FDR and higher coverage for credible sets in meta-analyses. We further illustrate our approach by applying it to a meta-analysis of Alzheimer’s disease genome-wide association studies where we prioritize putatively causal …