Coupling stochastic EM and Approximate Bayesian Computation for parameter inference in statespace models
Abstract
We study the class of statespace models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectationmaximization (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 SAEMABC 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 statespace model then a statespace 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.04831
 Bibcode:
 2015arXiv151204831P
 Keywords:

 Statistics  Computation;
 Statistics  Methodology
 EPrint:
 29 pages. Made a small fix to equation (8). Added the doi of the published version, doi: 10.1007/s001800170770y