Continuous-discrete smoothing of diffusions

Abstract

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 Schauer et al. (2017). We illustrate its efficiency in a number of challenging problems.

Revised article with additional author Marcin Mider. Article contains an animated figure

References in corpus (4)

• Exact simulation of diffusions
• Simulation of elliptic and hypo-elliptic conditional diffusions
• Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
• On residual and guided proposals for diffusion bridge simulation

Cited by in corpus (5)

• Control of Stochastic Quantum Dynamics by Differentiable Programming
• A piecewise deterministic Monte Carlo method for diffusion bridges
• Diffusion bridges for stochastic Hamiltonian systems and shape evolutions
• Automatic Backward Filtering Forward Guiding for Markov processes and graphical models
• Approximation of SPDE covariance operators by finite elements: A semigroup approach