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Optimal scaling of discrete approximations to Langevin diffusions.

Roberts, G. O. and Rosenthal, J. S. (1998) Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society - Series B: Statistical Methodology, 60 (1). pp. 255-268.

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Abstract

We consider the optimal scaling problem for proposal distributions in Hastings–Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.

Item Type: Article
Journal or Publication Title: Journal of the Royal Statistical Society - Series B: Statistical Methodology
Uncontrolled Keywords: Hastings–Metropolis algorithm • Langevin algorithm • Markov chain Monte Carlo method • Weak convergence
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Lancaster Environment Centre
ID Code: 19471
Deposited By: ep_ss_importer
Deposited On: 14 Nov 2008 16:55
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 15:30
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19471

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