Continuous-discrete smoothing of diffusions

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.

Automated summary

This study introduces a novel algorithm for sampling from the exact smoothing distribution and applies it to parameter estimation. The algorithm is called the BFFG algorithm. The method demonstrates efficiency in addressing several challenging problems.