Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions
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, 763-787. https://doi.org/10.1137/20M131549X
Published inSIAM/ASA Journal on Uncertainty Quantification
© 2021, Society for Industrial and Applied Mathematics
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. ...
PublisherSociety for Industrial & Applied Mathematics (SIAM)
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Research costs of Academy Research Fellow, AoF; Academy Project, AoF; Research post as Academy Research Fellow, AoF
Additional information about fundingJF, AJ, KL and MV have received support from the Academy of Finland (grants 274740, 312605 and 315619) and from the Institute for Mathematical Sciences, Singapore (2018 programme ‘Bayesian Computation for High-Dimensional Statistical Models’). NC and AJ have received support from KAUST baseline funding, JF and KL from The Alan Turing Institute, AJ from the Singapore Ministry of Education (R-155-000-161-112), and KL from the University of Manchester (School of Mathematics). ...
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