Continuous-discrete smoothing of diffusions

Journal article (2021)

Authors

Marcin Mider Trium Analysis Online GmbH
Moritz Schauer Chalmers University of Technology, University of Gothenburg
F.H. van der Meulen Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2021 Marcin Mider, Moritz Schauer, F.H. van der Meulen
DOI: https://doi.org/10.1214/21-EJS1894
Markov Chain Monte Carlo Filtering Data assimilation Diffusion bridge Chemical reaction network Guided proposal Lorenz system Partial observations Stochastic heat equation on a graph
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Published Date

2021

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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 [53]. We illustrate its efficiency in a number of challenging problems.