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dc.contributor.authorFranks, Jordan
dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J. H.
dc.contributor.authorVihola, Matti
dc.date.accessioned2020-01-13T13:09:26Z
dc.date.available2020-01-13T13:09:26Z
dc.date.issued2019-12-05
dc.identifier.urihttp://hdl.handle.net/10754/661006.1
dc.description.abstractWe develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give convergence results and recommend allocations for algorithm inputs. Our method admits a straightforward parallelisation, and can be computationally efficient. The user-friendly approach is illustrated on three examples, where the underlying diffusion is an Ornstein--Uhlenbeck process, a geometric Brownian motion, and a non-linear multivariate Pearson diffusion.
dc.description.sponsorshipJF, AJ, KL and MV have received support from the Academy of Finland (274740, 312605, 315619), as well as from the Institute for Mathematical Sciences, Singapore, during the 2018 programme ‘Bayesian Computation for High-Dimensional Statistical Models.’ AJ has received support from the Singapore Ministry of Education (R-155-000-161-112) and KL from the University of Manchester (School of Mathematics). JF and KL have received support from The Alan Turing Institute. This research made use of the Rocket High Performance Computing service at Newcastle University.
dc.language.isoen
dc.publisherSubmitted to Elsevier
dc.relation.urlhttps://arxiv.org/pdf/1807.10259
dc.rightsArchived with thanks to arXiv
dc.titleUnbiased inference for discretely observed hidden Markov model diffusions
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSubmitted to Stochastic Processes and their Applications
dc.eprint.versionPre-print
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
pubs.publication-statusSubmitted
dc.identifier.arxivid1807.10259
kaust.personJasra, Ajay
refterms.dateFOA2020-01-13T13:09:27Z
dc.date.posted2018-07-26


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