Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models

Umberto Picchini, Adeline Samson

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)

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 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.

Original languageEnglish
Pages (from-to)179-212
JournalComputational Statistics
Volume33
Issue number1
Early online date2017 Oct 23
DOIs
Publication statusPublished - 2018 Mar

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • Hidden Markov model
  • Maximum likelihood
  • Particle filter
  • SAEM
  • Sequential Monte Carlo
  • Stochastic differential equation

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