The summary-likelihood method and its implementation in the Infusion package

In recent years, simulation methods such as approximate Bayesian computation have extensively been used to infer parameters of population genetic models where the likelihood is intractable. We describe an alternative approach, summary likelihood, that provides a likelihood-based analysis of the information retained in the summary statistics whose distribution is simulated. We provide an automated implementation as a standard R package, Infusion, and we test the method, in particular for a scenario of inference of population-size change from genetic data. We show that the method provides confidence intervals with controlled coverage independently of a prior distribution on parameters, in contrast to approximate Bayesian computation. We expect the method to be applicable for at least six-parameter models and discuss possible modifications for higher-dimensional inference problems.