Beskos, Alexandros and Stuart, A. M. (2008) Optimal tuning of MCMC algorithms in infinite dimensions. In: (MCQMC'08) Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Montréal, Québec, 6-11 Jul 2008 (Unpublished)

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Abstract

We investigate local MCMC algorithms in infinite dimensions [1, 2, 3]. We are motivated by inverse problems in data assimilation, geophysics, and signal filtering/smoothing. For such complex problems, one can naturally select a linear (Gaussian) law to construct an a-priori distribution for the unknown (infinite-dimensional) parameters. We present Random-Walk Metropolis and Langevin algorithms to simulate from the a-posteriori distributions encompassing the data. We show that implicit methods for the derivation of the MCMC proposals are highly relevant in the context of the Gaussian reference measure. From another perspective, we find the optimal scaling for such local MCMC algorithms in high dimensions for general selections of reference measure. Our theory extends already established results for the iid case in the more realistic scenario of non-product target distributions.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Official Date:	8 July 2008
Dates:	Date Event 8 July 2008 Completion
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Conference Paper Type:	Paper
Title of Event:	(MCQMC'08) Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing
Type of Event:	Conference
Location of Event:	Montréal, Québec
Date(s) of Event:	6-11 Jul 2008

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