Progress with Uncertainty Quantification in generic Monte Carlo simulations

In the context of Monte Carlo (MC) simulation of particle transport the goal of Uncertainty Quantification (UQ) is to become able to predict how non statistical errors affect the physical outcomes: these errors derive mainly from uncertainties in the physics data and/or in the model they embed, but also from uncertainties in the description of the experimental configuration under examination. In the case of a single uncertainty a simple analytical relation exists among its the Probability Density Function (PDF) and the corresponding PDF for the output of the simulation: then a complete statistical analysis of the results of the simulation is always possible. The extension of this result to the multi-variate case is examined, when more than one of the physical input parameters are affected by uncertainties: a generalized analytical relation exists among input and output PDFs, but some more sophisticated mathematical tools are needed to handle such expression.