A central limit theorem for adaptive and interacting Markov chains

Abstract : Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions. In this paper, we study a general (non-Markovian) simulation framework covering both the adaptive and interacting MCMC algorithms. We establish a Central Limit Theorem for additive functionals of unbounded functions under a set of verifiable conditions, and identify the asymptotic variance. Our result extends all the results reported so far. An application to the interacting tempering algorithm (a simplified version of the equi-energy sampler) is presented to support our claims.
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Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2013, to be published
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https://hal.archives-ouvertes.fr/hal-00608569
Contributeur : Gersende Fort <>
Soumis le : mercredi 13 juillet 2011 - 14:19:32
Dernière modification le : jeudi 9 février 2017 - 15:19:22
Document(s) archivé(s) le : vendredi 14 octobre 2011 - 02:40:24

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  • HAL Id : hal-00608569, version 1
  • ARXIV : 1107.2574

Citation

Gersende Fort, Eric Moulines, Pierre Priouret, Pierre Vandekerkhove. A central limit theorem for adaptive and interacting Markov chains. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2013, to be published. <hal-00608569>

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