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A Dirichlet form approach to MCMC optimal scaling
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Zanella, Giacomo, Bedard, Mylene and Kendall, W. S. (2017) A Dirichlet form approach to MCMC optimal scaling. Stochastic Processes and their Applications, 127 (12). pp. 4053-4082. doi:10.1016/j.spa.2017.03.021 ISSN 0304-4149.
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Official URL: https://doi.org/10.1016/j.spa.2017.03.021
Abstract
This paper shows how the theory of Dirichlet forms can be used to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis–Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form methods have the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional distributions.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Dirichlet forms, Markov processes, Monte Carlo method | ||||||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||||||
Publisher: | Elsevier Science BV | ||||||||||||
ISSN: | 0304-4149 | ||||||||||||
Official Date: | 1 December 2017 | ||||||||||||
Dates: |
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Volume: | 127 | ||||||||||||
Number: | 12 | ||||||||||||
Page Range: | pp. 4053-4082 | ||||||||||||
DOI: | 10.1016/j.spa.2017.03.021 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 30 March 2017 | ||||||||||||
Date of first compliant Open Access: | 1 November 2017 | ||||||||||||
RIOXX Funder/Project Grant: |
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