Continuous-discrete smoothing of diffusions
Artikel i vetenskaplig tidskrift, 2021

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.

Guided proposal

Chemical reaction network

Lorenz system

Partial observations

Data assimilation

Stochastic heat equation on a graph


Diffusion bridge

Markov Chain Monte Carlo


Marcin Mider

Trium Analysis Online GmbH

Moritz Schauer

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Frank Van Der Meulen

TU Delft

Electronic Journal of Statistics

1935-7524 (ISSN)

Vol. 15 2 4295-4342



Sannolikhetsteori och statistik




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