Parameter estimation via conditional expectation: a Bayesian inversion

Hermann G. Matthies; Elmar Zander; Bojana V. Rosić; Alexander Litvinenko

doi:10.1186/s40323-016-0075-7

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 journal › Article › Academic › peer-review

28 Citations (Scopus)

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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 language	English
Article number	24
Journal	Advanced Modeling and Simulation in Engineering Sciences
Volume	3
Issue number	1
DOIs	https://doi.org/10.1186/s40323-016-0075-7
Publication status	Published - 1 Dec 2016
Externally published	Yes

Keywords

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

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10.1186/s40323-016-0075-7Licence: CC BY

Matthies2016parameterFinal published version, 2.08 MBLicence: CC BY

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KW - Conditional expectation

KW - Filters

KW - Functional and spectral approximation

KW - Inverse identification

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KW - Uncertainty quantification

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Parameter estimation via conditional expectation: a Bayesian inversion

Abstract

Keywords

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