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Coupling a stochastic approximation version of EM with an MCMC procedure. (English) Zbl 1155.62420

Summary: The stochastic approximation version of EM (SAEM) proposed by B. Delyon et al. [Ann. Stat. 27, No.1, 94–128 (1999; Zbl 0932.62094)] 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, 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 convolution models and change-point models are presented to illustrate the proposed method.

MSC:

62L20 Stochastic approximation
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains

Citations:

Zbl 0932.62094
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References:

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