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.

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}, pages = {115--131}, publisher = {EDP-Sciences}, volume = {8}, year = {2004}, doi = {10.1051/ps:2004007}, mrnumber = {2085610}, zbl = {1155.62420}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps:2004007/} }

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 SP - 115 EP - 131 VL - 8 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2004007/ DO - 10.1051/ps:2004007 LA - en ID - PS_2004__8__115_0 ER -

%0 Journal Article %A Kuhn, Estelle %A Lavielle, Marc %T Coupling a stochastic approximation version of EM with an MCMC procedure %J ESAIM: Probability and Statistics %D 2004 %P 115-131 %V 8 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2004007/ %R 10.1051/ps:2004007 %G en %F 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://archive.numdam.org/articles/10.1051/ps:2004007/

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