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Scaling limits for the transient phase.

Roberts, G. O. and Christian, O. and Rosenthal, J. S. (2005) Scaling limits for the transient phase. Journal of the Royal Statistical Society, Series B, 67 (2). pp. 253-268. ISSN 1467-9868

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Abstract

The paper considers high dimensional Metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk Metropolis algorithm, convergence during the transient phase is extremely regular—to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.

Item Type: Article
Journal or Publication Title: Journal of the Royal Statistical Society, Series B
Uncontrolled Keywords: Markov chain Monte Carlo methods • Metropolis–Hastings algorithm • Transient phase • Weak convergence
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Lancaster Environment Centre
ID Code: 19383
Deposited By: ep_ss_importer
Deposited On: 19 Nov 2008 16:20
Refereed?: Yes
Published?: Published
Last Modified: 06 Sep 2013 18:05
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19383

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