Unbiased Estimation of the Hessian for Partially Observed Diffusions
dc.contributor.author | Chada, Neil Kumar | |
dc.contributor.author | Jasra, Ajay | |
dc.contributor.author | Yu, Fangyuan | |
dc.date.accessioned | 2021-09-08T06:15:14Z | |
dc.date.available | 2021-09-08T06:15:14Z | |
dc.date.issued | 2021-09-06 | |
dc.identifier.uri | http://hdl.handle.net/10754/671103 | |
dc.description.abstract | In 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.sponsorship | This work was supported by KAUST baseline funding. | |
dc.publisher | arXiv | |
dc.relation.url | https://arxiv.org/pdf/2109.02371.pdf | |
dc.rights | Archived with thanks to arXiv under a CC-BY license. | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.title | Unbiased Estimation of the Hessian for Partially Observed Diffusions | |
dc.type | Preprint | |
dc.contributor.department | Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division | |
dc.contributor.department | Statistics | |
dc.eprint.version | Pre-print | |
dc.identifier.arxivid | 2109.02371 | |
kaust.person | Chada, Neil Kumar | |
kaust.person | Jasra, Ajay | |
kaust.person | Yu, Fangyuan | |
dc.relation.issupplementedby | github:fangyuan-ksgk/Hessian_Estimate | |
refterms.dateFOA | 2021-09-08T06:19:36Z | |
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.supportUnit | KAUST baseline funding |
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