Coupling a stochastic approximation version of EM with an MCMC procedure

Estelle Kuhn; Marc Lavielle

ESAIM: Probability and Statistics (2004)

  • Volume: 8, page 115-131
  • ISSN: 1292-8100

Abstract

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The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used to establish the convergence of SAEM when it is coupled with a Markov chain Monte-Carlo procedure. This result is very useful for many practical applications. Applications to the convolution model and the change-points model are presented to illustrate the proposed method.

How to cite

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Kuhn, Estelle, and Lavielle, Marc. "Coupling a stochastic approximation version of EM with an MCMC procedure." ESAIM: Probability and Statistics 8 (2004): 115-131. <http://eudml.org/doc/245020>.

@article{Kuhn2004,
abstract = {The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used to establish the convergence of SAEM when it is coupled with a Markov chain Monte-Carlo procedure. This result is very useful for many practical applications. Applications to the convolution model and the change-points model are presented to illustrate the proposed method.},
author = {Kuhn, Estelle, Lavielle, Marc},
journal = {ESAIM: Probability and Statistics},
keywords = {EM algorithm; SAEM algorithm; stochastic approximation; MCMC algorithm; convolution model; change-points model},
language = {eng},
pages = {115-131},
publisher = {EDP-Sciences},
title = {Coupling a stochastic approximation version of EM with an MCMC procedure},
url = {http://eudml.org/doc/245020},
volume = {8},
year = {2004},
}

TY - JOUR
AU - Kuhn, Estelle
AU - Lavielle, Marc
TI - Coupling a stochastic approximation version of EM with an MCMC procedure
JO - ESAIM: Probability and Statistics
PY - 2004
PB - EDP-Sciences
VL - 8
SP - 115
EP - 131
AB - The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used to establish the convergence of SAEM when it is coupled with a Markov chain Monte-Carlo procedure. This result is very useful for many practical applications. Applications to the convolution model and the change-points model are presented to illustrate the proposed method.
LA - eng
KW - EM algorithm; SAEM algorithm; stochastic approximation; MCMC algorithm; convolution model; change-points model
UR - http://eudml.org/doc/245020
ER -

References

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  11. [11] M. Lavielle and E. Moulines, A simulated annealing version of the EM algorithm for non-Gaussian deconvolution. Statist. Comput. 7 (1997) 229–236. 
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