Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions

Type
Article

Authors
Chada, Neil Kumar
Franks, Jordan
Jasra, Ajay
Law, Kody J H
Vihola, Matti

KAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

Preprint Posting Date
2018-07-26

Date
2021-06-08

Submitted Date
2020-01-27

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.

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

Acknowledgements
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.

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM/ASA Journal on Uncertainty Quantification

DOI
10.1137/20m131549x

arXiv
1807.10259

Additional Links
https://epubs.siam.org/doi/10.1137/20M131549X

Permanent link to this record

Version History

Now showing 1 - 2 of 2
VersionDateSummary
2*
2021-06-09 08:09:40
Published in journal
2020-01-13 13:09:26
* Selected version