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Stability of noisy Metropolis–Hastings
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Medina Aguayo, Felipe Javier, Lee, Anthony and Roberts, Gareth O. (2015) Stability of noisy Metropolis–Hastings. Statistics and Computing . pp. 1-25. doi:10.1007/s11222-015-9604-3 ISSN 0960-3174.
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Official URL: http://dx.doi.org/10.1007/s11222-015-9604-3
Abstract
Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that they target marginally the correct invariant distribution. However, the pseudo-marginal Markov chain can exhibit poor mixing and slow convergence towards its target. As an alternative, a subtly different Markov chain can be simulated, where better mixing is possible but the exactness property is sacrificed. This is the noisy algorithm, initially conceptualised as Monte Carlo within Metropolis, which has also been studied but to a lesser extent. The present article provides a further characterisation of the noisy algorithm, with a focus on fundamental stability properties like positive recurrence and geometric ergodicity. Sufficient conditions for inheriting geometric ergodicity from a standard Metropolis–Hastings chain are given, as well as convergence of the invariant distribution towards the true target distribution.
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): | Markov processes, Monte Carlo method | ||||||||
Journal or Publication Title: | Statistics and Computing | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0960-3174 | ||||||||
Official Date: | 7 November 2015 | ||||||||
Dates: |
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Number of Pages: | 25 | ||||||||
Page Range: | pp. 1-25 | ||||||||
DOI: | 10.1007/s11222-015-9604-3 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 28 January 2016 | ||||||||
Date of first compliant Open Access: | 8 February 2016 |
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