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Abstract: A genome-wide association study (GWAS) aims to determine genetic variants statistically associated with phenotypes. However, because of linkage disequilibrium (LD), a characteristic of large-scale genomic datasets referring to the strong local dependencies between single-nucleotide polymorphisms (SNPs), it is usually challenging to identify the actual causal variants among its associated proxies. In this work, we propose a Bayesian variable selection method called the sparse mixed Gaussian prior for generalized linear models (SMG-GLM). It is an efficient high-dimensional Bayesian variable selection approach designed for arbitrary relationships between variants and phenotypes. Besides, it calibrates the selection uncertainty by estimating posterior inclusion probabilities, which many popular variable selection methods do not address. We additionally combine the SMG-GLM with knockoffs, named SMG-knockoffs, to account for the collinearity problem caused by LD. The SMG-knockoffs method can make inferences on the variable selection result and control the false discovery rate at an expected level. Its competence in discovering causal variables while controlling a desired false discovery rate has been shown in simulation studies conducted on a GWAS dataset.