Open Access
2021 Continuous-discrete smoothing of diffusions
Marcin Mider, Moritz Schauer, Frank van der Meulen
Author Affiliations +
Electron. J. Statist. 15(2): 4295-4342 (2021). DOI: 10.1214/21-EJS1894


Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the process, consistent with the observations. We derive a novel Markov Chain Monte Carlo algorithm to sample from the exact smoothing distribution. The resulting algorithm is called the Backward Filtering Forward Guiding (BFFG) algorithm. We extend the algorithm to include parameter estimation. The proposed method relies on guided proposals introduced in [53]. We illustrate its efficiency in a number of challenging problems.

Funding Statement

The research leading to the results in this paper has received funding from the European Research Council under ERC Grant Agreement 320637. M.M. was sponsored by the Max Planck Institute for Mathematics in the Sciences, Leipzig and the EPSRC [grant number EP/L016710/1].


We thank the associate editor for valuable comments that considerably improved the contents and structure of the paper.


Download Citation

Marcin Mider. Moritz Schauer. Frank van der Meulen. "Continuous-discrete smoothing of diffusions." Electron. J. Statist. 15 (2) 4295 - 4342, 2021.


Received: 1 September 2020; Published: 2021
First available in Project Euclid: 14 September 2021

arXiv: 1712.03807
Digital Object Identifier: 10.1214/21-EJS1894

Primary: 60J60 , 65C05
Secondary: 62F15

Keywords: Chemical reaction network , data assimilation , diffusion bridge , Filtering , guided proposal , Lorenz system , Markov chain Monte Carlo , partial observations , stochastic heat equation on a graph

Vol.15 • No. 2 • 2021
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