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

TL;DR

This paper introduces a novel SAEM-ABC algorithm for parameter inference in state-space models, combining stochastic EM with approximate Bayesian computation and sequential Monte Carlo, demonstrating improved accuracy and performance in simulations.

Contribution

The paper develops a new SAEM-ABC algorithm that integrates ABC within SAEM using SMC, enhancing inference accuracy in complex state-space models.

Findings

SAEM-ABC can outperform bootstrap filter-based SAEM in certain scenarios.

The method provides accurate parameter estimates in nonlinear and stochastic differential equation models.

Comparisons show competitive or superior performance to iterated filtering and particle MCMC methods.

Abstract

We study the class of state-space models and perform maximum likelihood estimation for 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. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. 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. Comparisons with iterated filtering for maximum likelihood inference, and Gibbs sampling and particle marginal methods for Bayesian inference are presented.