dc.contributor.author Chada, Neil Kumar dc.contributor.author Franks, Jordan dc.contributor.author Jasra, Ajay dc.contributor.author Law, Kody J H dc.contributor.author Vihola, Matti dc.date.accessioned 2021-06-09T08:12:26Z dc.date.available 2020-01-13T13:09:26Z dc.date.available 2021-06-09T08:12:26Z dc.date.issued 2021-06-08 dc.date.submitted 2020-01-27 dc.identifier.citation Chada, N. K., Franks, J., Jasra, A., Law, K. J., & Vihola, M. (2021). Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions. SIAM/ASA Journal on Uncertainty Quantification, 9(2), 763–787. doi:10.1137/20m131549x dc.identifier.issn 2166-2525 dc.identifier.doi 10.1137/20m131549x dc.identifier.uri http://hdl.handle.net/10754/661006 dc.description.abstract We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretization bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretized approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomized multilevel Monte Carlo, and an importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretization as the number of Markov chain iterations increases. We give convergence results and recommend allocations for algorithm inputs. Our method admits a straightforward parallelization 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 2d nonreversible Langevin equation. dc.description.sponsorship The work of the first and third authors was supported by KAUST baseline funding. The work of the second, third, fourth, and fifth authors was supported by the Academy of Finland (grants 274740, 312605, and 315619) and by the Institute for Mathematical Sciences, Singapore (2018 programme Bayesian Computation for High-Dimensional Statistical Models""). The work of the second and fourth authors was also supported by The Alan Turing Institute. The work of the third author was also supported by the Singapore Ministry of Education (R-155-000-161-112). The work of the fourth author was also supported by the University of Manchester (School of Mathematics). This research made use of the Rocket High Performance Computing service at Newcastle University. dc.language.iso en dc.publisher Society for Industrial & Applied Mathematics (SIAM) dc.relation.url https://epubs.siam.org/doi/10.1137/20M131549X dc.rights Archived with thanks to SIAM/ASA Journal on Uncertainty Quantification dc.title Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions dc.type Article dc.contributor.department Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division dc.identifier.journal SIAM/ASA Journal on Uncertainty Quantification dc.eprint.version Post-print dc.contributor.institution School of Mathematics, Statistics and Physics, Newcastle University, Newcastle-upon-Tyne, NE1 7RU, UK. dc.contributor.institution School of Mathematics, University of Manchester, Manchester, M139PL, UK. dc.contributor.institution Department of Mathematics and Statistics, University of Jyv\ dc.identifier.volume 9 dc.identifier.issue 2 dc.contributor.affiliation King Abdullah University of Science and Technology (KAUST) dc.identifier.pages 763-787 pubs.publication-status Submitted dc.identifier.arxivid 1807.10259 kaust.person Chada, Neil Kumar kaust.person Jasra, Ajay dc.date.accepted 2021-03-08 refterms.dateFOA 2020-01-13T13:09:27Z kaust.acknowledged.supportUnit KAUST baseline funding dc.date.posted 2018-07-26
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