Publications [#199195] of Jonathan C. Mattingly

Papers Published

1. with Natesh S. Pillai, Andrew M. Stuart, Diffusion Limits of the Random Walk Metropolis Algorithm in High Dimensions, Annals of Applied Probability (June, 2011) [1003.4306]
   (last updated on 2011/12/12)

   Abstract:
   Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular they lead directly to 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. The purpose of this paper is to study 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. The diffusion limit of a random walk Metropolis algorithm to an infinite dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.