Framework for the correct treatment of model input parameters for Bayesian updating problems in nuclear engineering

Bayesian updating (BU) tools are increasingly used in nuclear engineering for inverse uncertainty quantification (IUQ) and calibration combined with uncertainty reduction. Their goals are quantifying or reducing the uncertainty of some of the uncertain model input parameters. Since it is often the case that available experimental data only allows for updating the most influential input parameters, researchers often ignore the less important ones during BU. This paper explores the consequences of neglecting the uncertainties of uncalibrated model input parameters (UMIP). It also proposes how to include them properly and which BU algorithms are the best choices for various types of inverse problems. The analysis is based on exploring two toy problems and one in nuclear engineering concerning multiplication factor calculations. The results clearly show that the improper treatment of UMIP during BU often leads to underestimating posterior uncertainties — either of the calibrated input parameters or the simulated integral parameters, depending on how the BU was conducted. The proposed methods of correct UMIP treatment will improve the rigorousness of the BU processes and boost confidence in the resulting posterior distributions.