Extension of Bayesian inference for multi-experimental and coupled problem in neutronics - a revisit of the theoretical approach

Bayesian methods are known for treating the so-called data re-assimilation. The Bayesian inference applied to core physics allows us to get a new adjustment of nuclear data using the results of integral experiments. This theory leading to reassimilation encompasses a broader approach. In previous papers, new methods have been developed to calculate the impact of nuclear and manufacturing data uncertainties on neutronics parameters. Usually, adjustment is performed step by step with one parameter and one experiment by batch. In this document, we rewrite Orlov theory to extend to multiple experimental values and parameters adjustment. We found that the multidimensional system expression looks like can be written as the mono-dimensional system in a matrix form. In this extension, correlation terms appears between experimental processes (manufacturing and measurements) and we discuss how to fix them. Then formula are applied to the extension to the Boltzmann/Bateman coupled problem, where each term could be evaluated by computing depletion uncertainties, studied in previous papers. (authors)