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 . We illustrate its efficiency in a number of challenging problems.
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.
"Continuous-discrete smoothing of diffusions." Electron. J. Statist. 15 (2) 4295 - 4342, 2021. https://doi.org/10.1214/21-EJS1894