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dc.contributor.authorChada, Neil Kumar
dc.contributor.authorJasra, Ajay
dc.contributor.authorYu, Fangyuan
dc.date.accessioned2022-06-23T05:57:08Z
dc.date.available2021-09-08T06:15:14Z
dc.date.available2022-06-23T05:57:08Z
dc.date.issued2022-06-22
dc.identifier.citationChada, N. K., Jasra, A., & Yu, F. (2022). Unbiased estimation of the Hessian for partially observed diffusions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2262). https://doi.org/10.1098/rspa.2021.0710
dc.identifier.issn1364-5021
dc.identifier.issn1471-2946
dc.identifier.doi10.1098/rspa.2021.0710
dc.identifier.urihttp://hdl.handle.net/10754/671103
dc.description.abstractIn this article, we consider the development of unbiased estimators of the Hessian, of the log-likelihood function with respect to parameters, for partially observed diffusion processes. These processes arise in numerous applications, where such diffusions require derivative information, either through the Jacobian or Hessian matrix. As time-discretizations of diffusions induce a bias, we provide an unbiased estimator of the Hessian. This is based on using Girsanov’s Theorem and randomization schemes developed through Mcleish (2011 Monte Carlo Methods Appl.17, 301–315 (doi:10.1515/mcma.2011.013)) and Rhee & Glynn (2016 Op. Res.63, 1026–1043). We demonstrate our developed estimator of the Hessian is unbiased, and one of finite variance. We numerically test and verify this by comparing the methodology here to that of a newly proposed particle filtering methodology. We test this on a range of diffusion models, which include different Ornstein–Uhlenbeck processes and the Fitzhugh–Nagumo model, arising in neuroscience.
dc.description.sponsorshipThis work was supported by KAUST baseline funding.
dc.publisherThe Royal Society
dc.relation.urlhttps://royalsocietypublishing.org/doi/10.1098/rspa.2021.0710
dc.rightsArchived with thanks to Proceedings of the Royal Society 2022 The Authors. Published by the Royal Society under the terms of theCreative Commons Attribution Licensehttp://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleUnbiased estimation of the Hessian for partially observed diffusions
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentStatistics
dc.identifier.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
dc.eprint.versionPublisher's Version/PDF
dc.identifier.volume478
dc.identifier.issue2262
dc.identifier.arxivid2109.02371
kaust.personChada, Neil Kumar
kaust.personJasra, Ajay
kaust.personYu, Fangyuan
dc.relation.issupplementedbygithub:fangyuan-ksgk/Hessian_Estimate
refterms.dateFOA2021-09-08T06:19:36Z
display.relations<b>Is Supplemented By:</b><br/> <ul><li><i>[Software]</i> <br/> Title: fangyuan-ksgk/Hessian_Estimate: Inference of PODPDO model through MLE on the estimation of the Jacobian & Hessian of data likelihood with respect to the unknown parameter.. Publication Date: 2021-06-22. github: <a href="https://github.com/fangyuan-ksgk/Hessian_Estimate" >fangyuan-ksgk/Hessian_Estimate</a> Handle: <a href="http://hdl.handle.net/10754/671186" >10754/671186</a></a></li></ul>
kaust.acknowledged.supportUnitBaseline funding


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Archived with thanks to Proceedings of the Royal Society 2022 The Authors. Published by the Royal Society under the terms of theCreative Commons Attribution Licensehttp://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
Except where otherwise noted, this item's license is described as Archived with thanks to Proceedings of the Royal Society 2022 The Authors. Published by the Royal Society under the terms of theCreative Commons Attribution Licensehttp://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
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