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Rendell, Lewis J., Johansen, Adam M., Lee, Anthony and Whiteley, Nick (2021) Global consensus Monte Carlo. Journal of Computational and Graphical Statistics, 30 (2). pp. 249-259. doi:10.1080/10618600.2020.1811105
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WRAP-Global-consensus-Monte-Carlo-Johansen-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1025Kb) | Preview |
Official URL: https://doi.org/10.1080/10618600.2020.1811105
Abstract
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science > Statistics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Monte Carlo method, Bayesian statistical decision theory, Markov processes | |||||||||||||||
| Journal or Publication Title: | Journal of Computational and Graphical Statistics | |||||||||||||||
| Publisher: | American Statistical Association | |||||||||||||||
| ISSN: | 1061-8600 | |||||||||||||||
| Official Date: | 2021 | |||||||||||||||
| Dates: |
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| Volume: | 30 | |||||||||||||||
| Number: | 2 | |||||||||||||||
| Page Range: | pp. 249-259 | |||||||||||||||
| DOI: | 10.1080/10618600.2020.1811105 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Publisher Statement: | “This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 08/09/2020, available online: http://www.tandfonline.com/10.1080/10618600.2020.1811105 | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| RIOXX Funder/Project Grant: |
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