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Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models

Graham, Matthew M.; Thiery, Alexandre H.; Beskos, Alexandros; (2022) Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 84 (4) pp. 1229-1256. 10.1111/rssb.12497. Green open access

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Abstract

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint configurations of the underlying process noise and of parameters, mapping onto diffusion paths consistent with observations, form an implicitly defined manifold. Then, by making use of a constrained Hamiltonian Monte Carlo algorithm on the embedded manifold, we are able to perform computationally efficient inference for a class of discretely observed diffusion models. Critically, in contrast with other approaches proposed in the literature, our methodology is highly automated, requiring minimal user intervention and applying alike in a range of settings, including: elliptic or hypo-elliptic systems; observations with or without noise; linear or non-linear observation operators. Exploiting Markovianity, we propose a variant of the method with complexity that scales linearly in the resolution of path discretisation and the number of observation times. Python code reproducing the results is available at http://doi.org/10.5281/zenodo.5796148.

Type: Article
Title: Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/rssb.12497
Publisher version: https://doi.org/10.1111/rssb.12497
Language: English
Additional information: © 2022 The Authors. Journal of the Royal Statistical Society: Series A (Statistics in Society) published by John Wiley & Sons Ltd on behalf of Royal Statistical Society. This is an open access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10141906
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