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Global consensus Monte Carlo

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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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Official URL: https://doi.org/10.1080/10618600.2020.1811105

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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:
DateEvent
2021Published
8 September 2020Available
3 August 2020Accepted
Volume: 30
Number: 2
Page Range: pp. 249-259
DOI: 10.1080/10618600.2020.1811105
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): “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:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N510129/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/M508184/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/R034710/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/T004134/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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