Adaptive Monte Carlo Markov Chains
Seminar Room 1, Newton Institute
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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