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Many statistical models of interest to the natural and social sciences have no tractable likelihood function. Until recently, Bayesian inference for such models was thought infeasible. Pritchard et al. (1999) introduced an algorithm known as ABC, for Approximate Bayesian Computation, that enables Bayesian computation in such models. Despite steady progress since this first breakthrough, such as the adaptation of MCMC and Sequential Monte Carlo techniques to likelihood-free inference, state-of-the art methods remain notoriously hard to use and require enormous computation times. Among other issues, one faces the difficult task of finding appropriate summary statistics for the model, and tuning the algorithm can be time-consuming when little prior information is available. We show that Expectation Propagation, a widely successful approximate inference technique, can be adapted to the likelihood-free context. The resulting algorithm does not require summary statistics, is an order of magnitude faster than existing techniques, and remains usable when prior information is vague.

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