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Coupling a stochastic approximation version of EMwith an MCMC procedure

Published online by Cambridge University Press:  15 September 2004

Estelle Kuhn  and
Marc Lavielle
Estelle Kuhn
Affiliation:
Université Paris Sud, Bât. 425, 91400 Orsay, France; Estelle.Kuhn@math.u-psud.fr.
Marc Lavielle
Affiliation:
Université René Descartes and Université Paris Sud, Bât. 425, 91400 Orsay, France; Marc.Lavielle@math.u-psud.fr.
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Abstract

The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) isa powerful alternative to EM when the E-step is intractable. Convergence ofSAEM toward a maximum of the observed likelihood is established whenthe unobserved data are simulated at each iteration under the conditionaldistribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximationwith Markovian perturbations are used to establish the convergenceof SAEM when it is coupled with a Markov chain Monte-Carloprocedure. 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 algorithmSAEM algorithmstochasticapproximationMCMC algorithmconvolution modelchange-points model.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 115 - 131
Copyright
© EDP Sciences, SMAI, 2004

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