Sequential Quasi-Monte Carlo: Introduction for Non-experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

Nicolas Chopin, Mathieu Gerber

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

Abstract

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (J R Stat Soc Ser B Stat Methodol 77(3):509–579, 2015, [16]) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.
Original languageEnglish
Title of host publicationMonte Carlo and Quasi-Monte Carlo Methods
Subtitle of host publicationMCQMC 2016, Stanford, CA, August 14-19
PublisherSpringer International Publishing AG
ISBN (Electronic)978-3-319-91436-7
ISBN (Print)978-3-319-91435-0
DOIs
Publication statusPublished - 2018

Keywords

  • Diffusion models
  • Particle filtering
  • Randomised quasi-Monte Carlo
  • Sequential Monte Carlo
  • State-space models

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