Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 84, Issue 4, Pages 1229-1256Publisher
WILEY
DOI: 10.1111/rssb.12497
Keywords
constrained dynamics; Hamiltonian Monte Carlo; partially observed diffusions; stochastic differential equations
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Funding
- Lloyd's Register Foundation programme on data-centric engineering at the Alan Turing Institute
- Singapore Ministry of Education Tier 2 [MOE2016-T2-2-135]
- Leverhulme Trust Prize
- Young Investigator Award Grant (NUSYIA) [FY16 P16, R-155-000-180-133]
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This paper proposes a method for inferring the posterior distribution of nonlinear diffusion processes observed at discrete times, using ideas from statistical physics and computational chemistry. The method is highly automated and applicable in a wide range of settings, outperforming other approaches in the literature.
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 .
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