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The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC
Univ Technol Sydney, Australia; Sveriges Riksbank, Sweden.
Univ Sydney, Australia.
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences. Stockholm Univ, Sweden.
Univ New South Wales, Australia.
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2021 (English)In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 30, no 4, p. 877-888Article in journal (Refereed) Published
Abstract [en]

Speeding upMarkov chainMonte Carlo (MCMC) for datasets withmany observations by data subsampling has recently received considerable attention. A pseudo-marginalMCMCmethod is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators, allowing us to update a single block of subsample indicators in each MCMC iteration so that a desired correlation is achieved between the logs of successive likelihood estimates. This is important since pseudo-marginal MCMC with positively correlated likelihood estimates can use substantially smaller subsamples without adversely affecting the sampling efficiency. The block-Poisson estimator is unbiased but not necessarily positive, so the algorithm runs the MCMC on the absolute value of the likelihood estimator and uses an importance sampling correction to obtain consistent estimates of the posterior mean of any function of the parameters. Our article derives guidelines to select the optimal tuning parameters for our method and shows that it compares very favorably to regular MCMC without subsampling, and to two other recently proposed exact subsampling approaches in the literature. Supplementary materials for this article are available online.

Place, publisher, year, edition, pages
Taylor & Francis, 2021. Vol. 30, no 4, p. 877-888
Keywords [en]
Bayesian inference; Control variates; Data subsampling; Exact inference; Poisson estimator; Pseudo-marginal MCMC
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-176860DOI: 10.1080/10618600.2021.1917420ISI: 000656806400001OAI: oai:DiVA.org:liu-176860DiVA, id: diva2:1571027
Note

Funding Agencies|Swedish Foundation for Strategic ResearchSwedish Foundation for Strategic Research [RIT 15-0097]; [CE140100049]

Available from: 2021-06-22 Created: 2021-06-22 Last updated: 2022-04-05

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