TY - JOUR
T1 - Parameter estimation via conditional expectation: a Bayesian inversion
AU - Matthies, Hermann G.
AU - Zander, Elmar
AU - Rosić, Bojana V.
AU - Litvinenko, Alexander
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Partly supported by the Deutsche Forschungsgemeinschaft (DFG) through SFB 880.
PY - 2016/8/11
Y1 - 2016/8/11
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/620945
UR - http://amses-journal.springeropen.com/articles/10.1186/s40323-016-0075-7
UR - http://www.scopus.com/inward/record.url?scp=85021037882&partnerID=8YFLogxK
U2 - 10.1186/s40323-016-0075-7
DO - 10.1186/s40323-016-0075-7
M3 - Article
SN - 2213-7467
VL - 3
JO - Advanced Modeling and Simulation in Engineering Sciences
JF - Advanced Modeling and Simulation in Engineering Sciences
IS - 1
ER -