A1 Journal article (refereed)
Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions (2021)

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. https://doi.org/10.1137/20M131549X

JYU authors or editors

Publication details

All authors or editors: Chada, Neil K.; Franks, Jordan; Jasra, Ajay; Law, Kody J.; Vihola, Matti

Journal or series: SIAM/ASA Journal on Uncertainty Quantification

eISSN: 2166-2525

Publication year: 2021

Volume: 9

Issue number: 2

Pages range: 763-787

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1137/20M131549X

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77469

Publication is parallel published: https://arxiv.org/pdf/1807.10259.pdf

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.

Keywords: mathematics; diffusion (physical phenomena); Bayesian analysis; Monte Carlo methods; Markov chains; mathematical methods; mathematical models

Free keywords: diffusion; importance sampling; Markov chain Monte Carlo; multilevel Monte Carlo; sequential Monte Carlo

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Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 1