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

Picchini, Umberto LU and Samson, Adeline (2017) In Computational Statistics
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... (More)

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.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Hidden Markov model, Maximum likelihood, Particle filter, SAEM, Sequential Monte Carlo, Stochastic differential equation
in
Computational Statistics
pages
34 pages
publisher
Physica Verlag
external identifiers
  • scopus:85031931657
ISSN
0943-4062
DOI
10.1007/s00180-017-0770-y
language
English
LU publication?
yes
id
05c383f3-7149-478a-a781-9be54b7956a9
alternative location
https://arxiv.org/abs/1512.04831
date added to LUP
2017-10-30 13:38:18
date last changed
2018-01-07 12:24:17
@article{05c383f3-7149-478a-a781-9be54b7956a9,
  abstract     = {<p>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.</p>},
  author       = {Picchini, Umberto and Samson, Adeline},
  issn         = {0943-4062},
  keyword      = {Hidden Markov model,Maximum likelihood,Particle filter,SAEM,Sequential Monte Carlo,Stochastic differential equation},
  language     = {eng},
  month        = {10},
  pages        = {34},
  publisher    = {Physica Verlag},
  series       = {Computational Statistics},
  title        = {Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models},
  url          = {http://dx.doi.org/10.1007/s00180-017-0770-y},
  year         = {2017},
}