2003 Prépublication d'Orsay numéro 2003-19 (07/11/2003)



COUPLING A STOCHASTIC APPROXIMATION VERSION OF EM WITH A MCMC PROCEDURE.

KUHN, Estelle - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
LAVIELLE, Marc - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : EM algorithm; SAEM algorithm; Stochastic approximation; MCMC algorithm; Convolution model; Change-points model.

Classification MSC : -


Resumé :

Abstract :
The stochastic approximation version of EM ( SAEM) proposed by Delyon et al. in [5] is a powerful alternative to EM when the E-step is untractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the non observed 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.

Contact : Marc.Lavielle@math.u-psud.fr