Evaluating extremely low p-values with importance sampling techniques in discovery-oriented HEP analyses.
Many results in current particle physics studies are derived using asymptotic approximations to calculate the p-value (or the significance) of the hypothesis tested. It is difficult to ensure to which extent the requirements for these approximations are valid in cases where the number of observations is not large, for binned fits with lowly populated bins or when there are non-gaussian nuisances with a significant contribution. The common alternative of estimation with pseudo-experiments becomes unattainable if the usual “5-sigma significance” is to be claimed.
A technique is proposed to overcome this problem, which permits a precise estimation of very low p-values with a modest number of pseudo-experiments for realistic cases and taking advantage of the expected signal model.