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dc.contributor.authorHeng, Jeremy
dc.contributor.authorHoussineau, Jeremie
dc.contributor.authorJasra, Ajay
dc.date.accessioned2021-05-31T08:15:40Z
dc.date.available2021-05-31T08:15:40Z
dc.date.issued2021-05-11
dc.identifier.urihttp://hdl.handle.net/10754/669314
dc.description.abstractWe consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the gradient of the log-likelihood function with respect to parameters, with no time-discretization bias. These estimators can be straightforwardly employed within stochastic gradient methods to perform maximum likelihood estimation or Bayesian inference. As our proposed methodology only requires access to a time-discretization scheme such as the Euler-Maruyama method, it is applicable to a wide class of diffusion processes and observation models. Our approach is based on a representation of the score as a smoothing expectation using Girsanov theorem, and a novel adaptation of the randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015], Jacob et al. [2020a]. This allows one to remove the time-discretization bias and burn-in bias when computing smoothing expectations using the conditional particle filter of Andrieu et al. [2010]. Central to our approach is the development of new couplings of multiple conditional particle filters. We prove under assumptions that our estimators are unbiased and have finite variance. The methodology is illustrated on several challenging applications from population ecology and neuroscience.
dc.description.sponsorshipAjay Jasra was supported by KAUST baseline funding. Jeremy Heng was funded by CY Initiative of Excellence (grant “Investissements d’Avenir” ANR-16-IDEX-0008).
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2105.04912.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectunbiased estimation
dc.subjectPartially-observed diffusions
dc.subjectparticle filters
dc.subjectcoupling, stochastic gradient methods
dc.subjectstochastic gradient methods
dc.titleOn Unbiased Score Estimation for Partially Observed Diffusions
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionESSEC Business School
dc.contributor.institutionUniversity of Warwick
dc.identifier.arxivid2105.04912
kaust.personJasra, Ajay
refterms.dateFOA2021-05-31T08:16:13Z
kaust.acknowledged.supportUnitKAUST baseline funding


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