Coupling a stochastic approximation version of EM with an MCMC procedure
ESAIM: Probability and Statistics, Volume 8 (2004), p. 115-131

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.

DOI : https://doi.org/10.1051/ps:2004007
Classification:  62F10,  62L20,  65C40
Keywords: EM algorithm, SAEM algorithm, stochastic approximation, MCMC algorithm, convolution model, change-points model
@article{PS_2004__8__115_0,
author = {Kuhn, Estelle and Lavielle, Marc},
title = {Coupling a stochastic approximation version of EM with an MCMC procedure},
journal = {ESAIM: Probability and Statistics},
publisher = {EDP-Sciences},
volume = {8},
year = {2004},
pages = {115-131},
doi = {10.1051/ps:2004007},
zbl = {1155.62420},
zbl = {pre02161878},
mrnumber = {2085610},
language = {en},
url = {http://www.numdam.org/item/PS_2004__8__115_0}
}

Kuhn, Estelle; Lavielle, Marc. Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM: Probability and Statistics, Volume 8 (2004) pp. 115-131. doi : 10.1051/ps:2004007. http://www.numdam.org/item/PS_2004__8__115_0/

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