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In nuclear reactor system design and safety analysis, the Best Estimate plusUncertainty (BEPU) methodology requires that computer model outputuncertainties must be quantified in order to prove that the investigated designstays within acceptance criteria. "Expert opinion" and "user self-evaluation"have been widely used to specify computer model input uncertainties in previousuncertainty, sensitivity and validation studies. Inverse UncertaintyQuantification (UQ) is the process to inversely quantify input uncertaintiesbased on experimental data in order to more precisely quantify such ad-hocspecifications of the input uncertainty information. In this paper, we usedBayesian analysis to establish the inverse UQ formulation, with systematic andrigorously derived metamodels constructed by Gaussian Process (GP). Due toincomplete or inaccurate underlying physics, as well as numerical approximationerrors, computer models always have discrepancy/bias in representing therealities, which can cause over-fitting if neglected in the inverse UQ process.The model discrepancy term is accounted for in our formulation through the"model updating equation". We provided a detailed introduction and comparisonof the full and modular Bayesian approaches for inverse UQ, as well as pointedout their limitations when extrapolated to the validation/prediction domain.Finally, we proposed an improved modular Bayesian approach that can avoidextrapolating the model discrepancy that is learnt from the inverse UQ domainto the validation/prediction domain.

Inverse Uncertainty Quantification using the Modular Bayesian Approach based on Gaussian Process, Part 1: Theory