Diffusion limits of the random walk metropolis algorithm in high dimensions
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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 mainly 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 occurring 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. © 2012 Institute of Mathematical Statistics.
Published Version (Please cite this version)10.1214/10-AAP754
Publication InfoMattingly, Jonathan Christopher; Pillai, NS; & Stuart, AM (2012). Diffusion limits of the random walk metropolis algorithm in high dimensions. Annals of Applied Probability, 22(3). pp. 881-890. 10.1214/10-AAP754. Retrieved from http://hdl.handle.net/10161/9523.
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Professor of Mathematics
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and