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    Unbiased inference for discretely observed hidden Markov model diffusions

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    Type
    Preprint
    Authors
    Franks, Jordan
    Jasra, Ajay cc
    Law, Kody J. H.
    Vihola, Matti
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-12-05
    Preprint Posting Date
    2018-07-26
    Permanent link to this record
    http://hdl.handle.net/10754/661006
    
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    Abstract
    We 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.
    Sponsors
    JF, 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.
    Publisher
    Submitted to Elsevier
    Journal
    Submitted to Stochastic Processes and their Applications
    arXiv
    1807.10259
    Additional Links
    https://arxiv.org/pdf/1807.10259
    Collections
    Preprints; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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