Applying approximate Bayesian computation to reduce uncertainty in multigroup 235-U cross-sections using ICSBEP experimental data

The multiplication factor (k_eff) and its uncertainty are critical design parameters in nuclear reactors. The k_eff uncertainty must be considered for operation, safety, and economic reasons. Consequently, reducing uncertainty in k_eff has been of interest to the nuclear industry for as long as nuclear reactors were designed. Two methods of reducing this uncertainty are in use – Generalized Linear Least Squares (GLLS) and A General Monte Carlo-Bayes Procedure for Improved Predictions of Integral Functions of Nuclear Data (MOCABA). Both methods have the ability to reduce the k_eff uncertainty by reducing uncertainty in cross-sections through the assimilation of measured critical systems’ or nuclear reactors’ operational data. The algorithms require means of simulating the experimental data and that the calibrated parameters are described by specific statistical distributions. GLLS is limited to linear models and multivariate normal prior and posterior, while MOCABA can use any (non-linear) model but is also limited to multivariate normal prior and posterior. This work implements a universal and rigorous algorithm called Sequential Monte Carlo – Approximate Bayesian Computation (SMC-ABC) for the same application. It is found that SMC-ABC, GLLS, and likely MOCABA give essentially the same results for the same problems. The paper also presents a reliable method for validating the results based on so-called “synthetic experiments”. Synthetic experiments are computationally generated data used in place of experiments. The method allows for verifying whether there is a risk of overfitting the calibrated parameters (cross-sections in case of this work) during the data assimilation. This novel method shows the potential of using SMC-ABC and other Bayesian calibration methods to generate improved general-purpose neutron cross-section libraries.