On the use of the BMC to resolve Bayesian inference with nuisance parameters

Nuclear data are widely used in many research fields. In particular, neutron-induced reaction cross sections play a major role in safety and criticality assessment of nuclear technology for existing power reactors and future nuclear systems as in Generation IV. Because both stochastic and deterministic codes are becoming very efficient and accurate with limited bias, nuclear data remain the main uncertainty sources. A worldwide effort is done to make improvement on nuclear data knowledge thanks to new experiments and new adjustment methods in the evaluation processes. This paper gives an overview of the evaluation processes used for nuclear data at CEA. After giving Bayesian inference and associated methods used in the CONRAD code [P. Archier et al., Nucl. Data Sheets 118, 488 (2014)], a focus on systematic uncertainties will be given. This last can be deal by using marginalization methods during the analysis of differential measurements as well as integral experiments. They have to be taken into account properly in order to give well-estimated uncertainties on adjusted model parameters or multigroup cross sections. In order to give a reference method, a new stochastic approach is presented, enabling marginalization of nuisance parameters (background, normalization...). It can be seen as a validation tool, but also as a general framework that can be used with any given distribution. An analytic example based on a fictitious experiment is presented to show the good ad-equations between the stochastic and deterministic methods. Advantages of such stochastic method are meanwhile moderated by the time required, limiting it's application for large evaluation cases. Faster calculation can be foreseen with nuclear model implemented in the CONRAD code or using bias technique. The paper ends with perspectives about new problematic and time optimization