Nuclear reaction modeling has been continuously being improved for many decades now. That's especially the case for our nuclear cascade code INCL. An ANR project has been funded for the next four years (2024-2027) to work on the issue of uncertainty and error estimate. Since this code is implemented in the particle transport code Geant4, the next step is to propagate these uncertainties from INCL to Geant4. There was a recent study on uncertainty propagation, called Transport Monte Carlo (TMC). However, this study only addresses the propagation of uncertainties related to model parameters, there was no propagation of model biases (related to hypotheses) and their uncertainties, which are both outside the physical model. Therefore, the propagation of biases and their uncertainties, which are coming from Monte Carlo collision models, is unexplored territory. The aim of the proposed PhD project is then to develop methods for this kind of propagation and to study the functioning and features of the developed methods in schematic scenarios. The full implementation of the developed methods into a transport code, such as GEANT4, however, is not within the core scope of the thesis, but it might be possible if time permits.