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The Block-Poisson Estimator for Optimally Tuned Exact Subsampling MCMC
Univ Technol Sydney, Australia; Sveriges Riksbank, Sweden.
Univ Sydney, Australia.
Linköpings universitet, Institutionen för datavetenskap, Statistik och maskininlärning. Linköpings universitet, Filosofiska fakulteten. Stockholm Univ, Sweden.
Univ New South Wales, Australia.
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2021 (Engelska)Ingår i: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 30, nr 4, s. 877-888Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Taylor & Francis, 2021. Vol. 30, nr 4, s. 877-888
Nyckelord [en]
Bayesian inference; Control variates; Data subsampling; Exact inference; Poisson estimator; Pseudo-marginal MCMC
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
URN: urn:nbn:se:liu:diva-176860DOI: 10.1080/10618600.2021.1917420ISI: 000656806400001OAI: oai:DiVA.org:liu-176860DiVA, id: diva2:1571027
Anmärkning

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

Tillgänglig från: 2021-06-22 Skapad: 2021-06-22 Senast uppdaterad: 2022-04-05

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Villani, Mattias
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Statistik och maskininlärningFilosofiska fakulteten
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Journal of Computational And Graphical Statistics
Sannolikhetsteori och statistik

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