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The increasing availability of population-level allele frequency data acrossone or more related populations necessitates the development of methods thatcan efficiently estimate population genetics parameters, such as the strengthof selection acting on the population(s), from such data. Existing methods forthis problem in the setting of the Wright-Fisher diffusion model are primarilylikelihood-based, and rely on numerical approximation for likelihoodcomputation and on bootstrapping for assessment of variability in the resultingestimates, requiring extensive computation. Recent work (Jenkins and Spano,2015) has provided a method for obtaining exact samples from generalWright-Fisher diffusion processes, enabling the development of methods forBayesian estimation in this setting. We develop and implement a Bayesian methodfor estimating the strength of selection based on the Wright-Fisher diffusionfor data sampled at a single time point. The method utilizes the work ofJenkins and Spano (2015) to develop a Markov chain Monte Carlo algorithm todraw samples from the joint posterior distribution of the selection coefficientand the allele frequencies. We demonstrate that when assumptions about theinitial allele frequencies are accurate the method performs well for bothsimulated data and for an empirical data set on hypoxia in flies (Zhou et al.2011), where we find evidence for strong positive selection in a region ofchromosome 2L previously identified by Ronen et al. (2013). We discuss possibleextensions of our method to the more general settings commonly encountered inpractice, highlighting the advantages of Bayesian approaches to inference inthis setting.

Bayesian Inference of Selection in the Wright-Fisher Diffusion Model