Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in state-space models

We study the class of state-space models and perform maximum likelihood inference on the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on sequential Monte Carlo (SMC) methodology. Two simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation. It is shown that the ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. Comparisons with iterated filtering for maximum likelihood inference and particle marginal methods for Bayesian inference are presented.