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dc.contributor.authorChada, Neil Kumar
dc.contributor.authorJasra, Ajay
dc.contributor.authorYu, Fangyuan
dc.date.accessioned2021-09-08T06:15:14Z
dc.date.available2021-09-08T06:15:14Z
dc.date.issued2021-09-06
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] and Rhee & Glynn [2015]. 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.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2109.02371.pdf
dc.rightsArchived with thanks to arXiv under a CC-BY license.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleUnbiased Estimation of the Hessian for Partially Observed Diffusions
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentStatistics
dc.eprint.versionPre-print
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.supportUnitKAUST baseline funding


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Archived with thanks to arXiv under a CC-BY license.
Except where otherwise noted, this item's license is described as Archived with thanks to arXiv under a CC-BY license.