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Diffusions limits of the Random Walk Metropolis Algorithm in High Dimensions:

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Metropolis-Hastings methods form a widely used class of MCMC methods for sampling from complex probability distributions. Diffusion limits of MCMC methods (obtained by a invariance principle argument) in high dimensions provide a useful theoretical tool for studying efficiency. In particular they facilitate precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have only been proved for target measures with a product structure, severely limiting their applicability to real applications. In this talk, we will discuss diffusion limits for a class of naturally occuring high dimensional measures, found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure.

This talk is part of the Statistics series.

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