Dimension reduction in statistical estimation of partially observed multiscale processes

Andrew Papanicolaou, Konstantinos Spiliopoulos

Research output: Contribution to journalArticlepeer-review

Abstract

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced dimension. Then, this result is used to justify statistical estimation for the unknown parameters of interest based on the model of reduced dimension but using the original available data. This allows us to learn the unknown parameters of interest while working in lower dimensions, as opposed to working with the original high dimensional system. Simulation studies support and illustrate the theoretical results.

Original languageEnglish (US)
Pages (from-to)1220-1247
Number of pages28
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume5
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Data assimilation
  • Dimension reduction
  • Filtering
  • Homogenization
  • Multiscale diffusions
  • Parameter estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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