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dc.contributor.authorChada, Neil Kumar
dc.contributor.authorFranks, Jordan
dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J H
dc.contributor.authorVihola, Matti
dc.date.accessioned2021-06-09T08:12:26Z
dc.date.available2020-01-13T13:09:26Z
dc.date.available2021-06-09T08:12:26Z
dc.date.issued2021-06-08
dc.date.submitted2020-01-27
dc.identifier.citationChada, N. K., Franks, J., Jasra, A., Law, K. J., & Vihola, M. (2021). Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions. SIAM/ASA Journal on Uncertainty Quantification, 9(2), 763–787. doi:10.1137/20m131549x
dc.identifier.issn2166-2525
dc.identifier.doi10.1137/20m131549x
dc.identifier.urihttp://hdl.handle.net/10754/661006
dc.description.abstractWe develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretization bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretized approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomized multilevel Monte Carlo, and an importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretization as the number of Markov chain iterations increases. We give convergence results and recommend allocations for algorithm inputs. Our method admits a straightforward parallelization and can be computationally efficient. The user-friendly approach is illustrated on three examples, where the underlying diffusion is an Ornstein--Uhlenbeck process, a geometric Brownian motion, and a 2d nonreversible Langevin equation.
dc.description.sponsorshipThe work of the first and third authors was supported by KAUST baseline funding. The work of the second, third, fourth, and fifth authors was supported by the Academy of Finland (grants 274740, 312605, and 315619) and by the Institute for Mathematical Sciences, Singapore (2018 programme ``Bayesian Computation for High-Dimensional Statistical Models""). The work of the second and fourth authors was also supported by The Alan Turing Institute. The work of the third author was also supported by the Singapore Ministry of Education (R-155-000-161-112). The work of the fourth author was also supported by the University of Manchester (School of Mathematics). This research made use of the Rocket High Performance Computing service at Newcastle University.
dc.language.isoen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttps://epubs.siam.org/doi/10.1137/20M131549X
dc.rightsArchived with thanks to SIAM/ASA Journal on Uncertainty Quantification
dc.titleUnbiased Inference for Discretely Observed Hidden Markov Model Diffusions
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM/ASA Journal on Uncertainty Quantification
dc.eprint.versionPost-print
dc.contributor.institutionSchool of Mathematics, Statistics and Physics, Newcastle University, Newcastle-upon-Tyne, NE1 7RU, UK.
dc.contributor.institutionSchool of Mathematics, University of Manchester, Manchester, M139PL, UK.
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Jyv\
dc.identifier.volume9
dc.identifier.issue2
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.pages763-787
pubs.publication-statusSubmitted
dc.identifier.arxivid1807.10259
kaust.personChada, Neil Kumar
kaust.personJasra, Ajay
dc.date.accepted2021-03-08
refterms.dateFOA2020-01-13T13:09:27Z
kaust.acknowledged.supportUnitKAUST baseline funding
dc.date.posted2018-07-26


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