Likelihood-free stochastic approximation EM for inference in complex models

A new maximum likelihood methodology for the parameters of incomplete data models is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters, with the novelty of using synthetic likelihoods within SAEM. While SAEM is best suited for models having a tractable complete likelihood function, its application to moderately complex models is a difficult task, resulting impossible for models having so-called intractable likelihoods. The latter are typically treated with approximate Bayesian computation (ABC) algorithms or synthetic likelihoods (SL), where information about parameters contained in the data is encoded into summary statistics. While ABC is considered the state-of-art methodology for intractable likelihoods, its algorithms are often difficult to tune. By exploiting the Gaussian assumption set by SL on data summaries, we can construct a likelihood-free version of SAEM where sufficient statistics for the "synthetic complete likelihood" are automatically obtained via simulation. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models, the ability to simulate realizations from the model being the only requirement. The method is tested on three simulation studies.