Credible fission gas release calibration: A hierarchical Metropolis–Hastings-within-Gibbs approach to address model inadequacy

This work introduces a comprehensive and statistically robust framework for quantifying model parameter uncertainties in nuclear fuel performance predictions, ensuring that all sources of discrepancy (e.g., measurement noise, parameter variability, and model inadequacy) are systematically captured. Parameter uncertainties are essential inputs to safety analyses and are typically obtained through calibration; however, standard Bayesian calibration often underestimates uncertainty when the underlying model cannot fully reproduce experimental observations. To overcome this limitation, we employ a hierarchical probabilistic formulation in which model parameters vary according to distributions governed by both local experiment-specific and global hyperparameters, thereby explicitly accounting for unmodeled variability and structural deficiencies in the model. This paper demonstrates the practical implementation of this approach using an efficient Metropolis-Hastings-within-Gibbs sampling to calibrate a fission gas release model in the fuel performance code TRANSURANUS against Westinghouse’s commercial database. The resulting posteriors provide uncertainty estimates that credibly span all code-to-measurement discrepancies, remain robust across linear and nonlinear models, and directly support safety evaluations by offering defensible uncertainty margins. This approach establishes a generalizable pathway for uncertainty quantification in fuel performance modeling and enhances confidence in predictive simulations to inform high-consequence decisions.