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dc.contributor.authorChada, Neil K.
dc.contributor.authorFranks, Jordan
dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J.
dc.contributor.authorVihola, Matti
dc.date.accessioned2021-08-24T06:29:56Z
dc.date.available2021-08-24T06:29:56Z
dc.date.issued2021
dc.identifier.citationChada, N. K., Franks, J., Jasra, A., Law, K. J., & Vihola, M. (2021). Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions. <i>SIAM/ASA Journal on Uncertainty Quantification</i>, <i>9</i>, 763-787. <a href="https://doi.org/10.1137/20M131549X" target="_blank">https://doi.org/10.1137/20M131549X</a>
dc.identifier.otherCONVID_98936174
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/77469
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.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.ispartofseriesSIAM/ASA Journal on Uncertainty Quantification
dc.rightsIn Copyright
dc.subject.otherdiffusion
dc.subject.otherimportance sampling
dc.subject.otherMarkov chain Monte Carlo
dc.subject.othermultilevel Monte Carlo
dc.subject.othersequential Monte Carlo
dc.titleUnbiased Inference for Discretely Observed Hidden Markov Model Diffusions
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202108244634
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineTilastotiedefi
dc.contributor.oppiaineStatisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange763-787
dc.relation.issn2166-2525
dc.relation.volume9
dc.type.versionacceptedVersion
dc.rights.copyright© 2021, Society for Industrial and Applied Mathematics
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber312605
dc.relation.grantnumber315619
dc.relation.grantnumber274740
dc.subject.ysomatematiikka
dc.subject.ysoMonte Carlo -menetelmät
dc.subject.ysomatemaattiset mallit
dc.subject.ysobayesilainen menetelmä
dc.subject.ysoMarkovin ketjut
dc.subject.ysomatemaattiset menetelmät
dc.subject.ysodiffuusio (fysikaaliset ilmiöt)
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
jyx.subject.urihttp://www.yso.fi/onto/yso/p6361
jyx.subject.urihttp://www.yso.fi/onto/yso/p11401
jyx.subject.urihttp://www.yso.fi/onto/yso/p17803
jyx.subject.urihttp://www.yso.fi/onto/yso/p13075
jyx.subject.urihttp://www.yso.fi/onto/yso/p1880
jyx.subject.urihttp://www.yso.fi/onto/yso/p18009
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1137/20M131549X
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiatutkijan tutkimuskulut, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramResearch costs of Academy Research Fellow, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundinginformationJF, AJ, KL and MV have received support from the Academy of Finland (grants 274740, 312605 and 315619) and from the Institute for Mathematical Sciences, Singapore (2018 programme ‘Bayesian Computation for High-Dimensional Statistical Models’). NC and AJ have received support from KAUST baseline funding, JF and KL from The Alan Turing Institute, AJ from the Singapore Ministry of Education (R-155-000-161-112), and KL from the University of Manchester (School of Mathematics).


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