Bayesian updating for data adjustments and multi-level uncertainty propagation within Total Monte Carlo

In this work, a method is proposed for combining differential and integral benchmark experimental data within a Bayesian framework for nuclear data adjustments and multi-level uncertainty propagation using the Total Monte Carlo method. First, input parameters to basic nuclear physics models implemented within the state of the art nuclear reactions code, TALYS, were sampled from uniform distributions and randomly varied to produce a large set of random nuclear data files. Next, a probabilistic data assimilation was carried out by computing the likelihood function for each random nuclear data file based first on only differential experimental data (1st update) and then on integral benchmark data (2nd update). The individual likelihood functions from the two updates were then combined into a global likelihood function which was used for the selection of the final 'best' file. The proposed method has been applied for the adjustment of $^{208}$Pb in the fast neutron energy region below 20 MeV. The 'best' file from the adjustments was compared with available experimental data from the EXFOR database as well as evaluations from the major nuclear data libraries and found to compare favourably.