In this work we present expressions for the Variational Mean Field Approximation (VMFA) of the model described in Hormozdiari et al. Identifying Causal Variants at Loci with Multiple Signals of Association. Genetics, Vol. 198, 497–508(2014). We claim that the VMFA is not going to compromise accuracy and is going to improve speed on the calculation of the confidence sets of causal variants.