Bayesian Model Averaging (BMA) for nuclear data evaluation

Abstract

To ensure agreement between theoretical calculations and experimental data, parameters to selected nuclear physics models, are perturbed, and fine-tuned in nuclear data evaluations. This approach assumes that the chosen set of models accurately represents the `true' distribution. Furthermore, the models are chosen globally, indicating their applicability across the entire energy range of interest. However, this approach overlooks uncertainties inherent in the models themselves. As a result, achieving satisfactory fits to experimental data within certain energy regions for specific channels becomes challenging, as the evaluation is constrained by the deficiencies of the selected models. In this work, we propose that instead of selecting globally a winning model set and proceeding with it as if it was the `true' model set, we instead, take a weighted average over multiple models within a BMA framework, each weighted by its posterior probability. The method involves executing a set of TALYS calculations by randomly varying multiple nuclear physics models and their parameters to yield a vector of calculated observables. Next, the likelihood function was computed at each considered incident energy point for selected cross sections by comparing the vector of calculated observables with that of the selected differential experimental data. As the cross sections and elastic angular distributions were updated locally on a per-energy-point basis, the approach typically results in discontinuities or "kinks" in the curves, and these were addressed using spline interpolation. The proposed BMA method was applied to the evaluation of proton induced reactions on $^{58}$Ni within 1 - 100 MeV. The results demonstrate favorable comparisons with experimental data, as well as with the TENDL-2021 evaluation.