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Adaptive Monte Carlo Markov Chains

Presented by: 
E Moulines [CNRS]
Friday 20th June 2008 - 11:30 to 12:30
INI Seminar Room 1

In this talk, we present in a common unifying framework several adaptive Monte Carlo Markov chain algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the Independent Metropolis-Hastings algorithm and the Random Walk Metropolis algorithm with symmetric increments. Finally we propose an application of these results to the case where the proposal distribution of the Metropolis-Hastings update is a mixture of distributions from a curved exponential family. Several illustrations will be provided.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons