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Scalable importance tempering and Bayesian variable selection
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Zanella, Giacomo and Roberts, Gareth O. (2019) Scalable importance tempering and Bayesian variable selection. Journal of the Royal Statistical Society : Series B (Statistical Methodology), 81 (3). pp. 489-517. doi:10.1111/rssb.12316 ISSN 1369-7412.
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Official URL: https://doi.org/10.1111/rssb.12316
Abstract
We propose a Monte Carlo algorithm to sample from high-dimensional probability distributions that combines Markov chain Monte Carlo (MCMC) and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high-dimensionality, explicit comparison with standard MCMC and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard ones. When applied to Bayesian Variable Selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and allows to perform fast and reliable fully Bayesian inferences with tens of thousand regressors.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Monte Carlo method, Markov processes, Algorithms | ||||||||||||
Journal or Publication Title: | Journal of the Royal Statistical Society : Series B (Statistical Methodology) | ||||||||||||
Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||||||
ISSN: | 1369-7412 | ||||||||||||
Official Date: | July 2019 | ||||||||||||
Dates: |
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Volume: | 81 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 489-517 | ||||||||||||
DOI: | 10.1111/rssb.12316 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Zanella, G. and Roberts, G. (2019), Scalable importance tempering and Bayesian variable selection. J. R. Stat. Soc. B. which has been published in final form at doi:10.1111/rssb.12316. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 1 March 2019 | ||||||||||||
Date of first compliant Open Access: | 27 March 2020 | ||||||||||||
RIOXX Funder/Project Grant: |
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