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An exact framework for uncertainty quantification in Monte Carlo simulation

In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in the physics data and/or in the model they embed. 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: this allows a complete statistical analysis of the results of the simulation. We examine the extension of this result to the multi-variate case, when more than one of the physical input parameters are affected by uncertainties: a typical scenario is the prediction of the dependence of the simulation on input cross section tabulations.