Unbiased estimation of the Hessian for partially observed diffusions

Neil Kumar Chada, Ajay Jasra, Fangyuan Yu

Research output: Contribution to journalArticlepeer-review


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 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.
Original languageEnglish (US)
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2262
StatePublished - Jun 22 2022

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Engineering(all)
  • Mathematics(all)


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