Math @ Duke

Publications [#303553] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 with Mattingly, JC; Pillai, NS; Stuart, AM, Diffusion limits of the random walk Metropolis algorithm in high
dimensions,
Annals of Applied Probability, vol. 22 no. 3
(June, 2011),
pp. 881930, Institute of Mathematical Statistics [1003.4306], [1003.4306v4], [doi]
(last updated on 2021/05/10)
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 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 highdimensional 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 infinitedimensional Hilbert space valued SDE (or SPDE) is proved,
facilitating understanding of the computational complexity of the algorithm.


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