Parameter estimation via conditional expectation: a Bayesian inversion

Hermann G. Matthies*, Elmar Zander, Bojana V. Rosić, Alexander Litvinenko

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

20 Citations (Scopus)
12 Downloads (Pure)

Abstract

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp. functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by actual observations of the response of the real system. In a probabilistic setting, Bayes’s theory is the proper mathematical background for this identification process. The possibility of being able to compute a conditional expectation turns out to be crucial for this purpose. We show how this theoretical background can be used in an actual numerical procedure, and shortly discuss various numerical approximations.

Original languageEnglish
Article number24
JournalAdvanced Modeling and Simulation in Engineering Sciences
Volume3
Issue number1
DOIs
Publication statusPublished - 1 Dec 2016
Externally publishedYes

Keywords

  • Bayesian update
  • Conditional expectation
  • Filters
  • Functional and spectral approximation
  • Inverse identification
  • Parameter identification
  • Uncertainty quantification

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