Continuous-discrete smoothing of diffusions

Marcin Mider, Moritz Schauer, Frank van der Meulen

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Pages (from-to)4295-4342
Number of pages48
JournalElectronic Journal of Statistics
Volume15
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • Chemical reaction network
  • Data assimilation
  • Diffusion bridge
  • Filtering
  • Guided proposal
  • Lorenz system
  • Markov Chain Monte Carlo
  • Partial observations
  • Stochastic heat equation on a graph

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