Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models
(2018) In Computational Statistics 33(1). p.179-212- 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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- author
- Picchini, Umberto LU and Samson, Adeline
- organization
- publishing date
- 2018-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hidden Markov model, Maximum likelihood, Particle filter, SAEM, Sequential Monte Carlo, Stochastic differential equation
- in
- Computational Statistics
- volume
- 33
- issue
- 1
- pages
- 179 - 212
- publisher
- Physica Verlag
- external identifiers
-
- scopus:85031931657
- ISSN
- 0943-4062
- DOI
- 10.1007/s00180-017-0770-y
- project
- Stochastic modelling of protein folding and likelihood-free statistical inference methods
- 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
- 2022-04-25 03:36:10
@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}}, keywords = {{Hidden Markov model; Maximum likelihood; Particle filter; SAEM; Sequential Monte Carlo; Stochastic differential equation}}, language = {{eng}}, number = {{1}}, pages = {{179--212}}, 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}}, doi = {{10.1007/s00180-017-0770-y}}, volume = {{33}}, year = {{2018}}, }