Uncertainty Quantification in Monte Carlo Simulation: Theoretical Foundations and Heuristic Investigations

¹ INFN, Sezione di Genova, Via Dodecaneso 33, Genova, Italy 16146
² Jozef Stefan Institute, Jamova cesta 39, Ljubljana, Slovenia 1000

Abstract

We present advances in the development of methods to predict the effect that uncertainties in physical data needed for generic Monte Carlo simulations induce on the observables resulting from the simulation. Under wide conditions the PDF for the input (uncertain) physical data determine univocally the PDF for the output of the simulation: this general result has clear and powerful applications both in the case of a single (or few) uncertain input data and in the case of many unknown variables, provided they are totally correlated or uncorrelated. Although this is a typical example of forward propagation problem, our results can be applicable also in the backward case, for instance when one is trying to assess conditions for a robust design.