Likelihood-Free Inference for Direct Observations of a Scalar Stationary Wright--Fisher Diffusion

We consider the problem of inferring the mutation parameters from a discretely observed scalar Wright--Fisher diffusion through the use of likelihood-free methods. We propose an adaptive approximate Bayesian computation scheme, where previously accepted parameter draws inform those in subsequent iterations. We provide empirical evidence that the method recovers the true data generating parameters, even when using a non-sufficient summary statistic.