Parameter estimation via conditional expectation: a Bayesian inversion

H.G. Matthies, E. Zander, B.V. Rosić, A. Litvinenko
Advanced Modeling and Simulation in Engineering Sciences, 3(1), 24, (2016)

Parameter estimation via conditional expectation: a Bayesian inversion

Keywords

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

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.

Code

DOI: 10.1186/s40323-016-0075-7

Sources

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