Continuous-discrete smoothing of diffusions
Journal article, 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
Filtering
Diffusion bridge
Markov Chain Monte Carlo
Author
Marcin Mider
Trium Analysis Online GmbH
Moritz Schauer
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Frank Van Der Meulen
Delft University of Technology
Electronic Journal of Statistics
1935-7524 (ISSN)
Vol. 15 2 4295-4342Subject Categories
Computational Mathematics
Probability Theory and Statistics
Control Engineering
DOI
10.1214/21-EJS1894