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Optimal Monte Carlo Sampling and a Multi-Core Metropolis-Hastings Algorithm

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Abstract. When tasked with drawing approximate samples from a distribution of interest, perhaps the most commonly-used approach is the Metropolis-Hastings algorithm, a Markov Chain Monte Carlo (MCMC)technique. In this method, one proceeds by i) proposing moves to new locations, and then ii) deciding whether or not to accept these proposals. A key tradeoff with such algorithms concerns how ambitious to be with these proposal moves; one prefers to make large moves when possible, but one also wants to have a reasonable proportion of proposal moves accepted.

In this talk, I will review a framework which has provided practically useful answers on how to navigate this tradeoff, the theory of `optimal scaling’ for MCMC .I will then discuss recent work on how this theory can be adapted to the scenario in which parallel computing resources are available, and describe how one can use them to improve the efficiency of standard MCMC algorithms. This leads to concrete practical recommendations, as well as providing some quantitative estimates for how much benefit one can asymptotically expect from parallelism.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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