Statistical Methods for the Search of Sterile Neutrinos
The statistical methods applied to search for short-baseline neutrino oscillations induced by a sterile neutrino with mass at the eV scale are reviewed and compared. The comparison is performed under limit setting and signal discovery scenarios, considering both when an oscillation would enhance the neutrino interaction rate in the detector and when it would reduce it. The sensitivity of the experiments and the confidence regions extracted for specific data sets are found to change significantly according to the test statistic used for the hypothesis testing. The most general test statistic does not make assumptions on the value of the parameters of interest for the analysis, while the others restrict the allowed parameter space. The restriction of the parameter space could lead to miss a signal or, vice versa, to claim a discovery when this is not statistically significant. Similar issues are found also when the validity of Wilks' theorem is assumed. A standardized analysis approach based on the most general kind of hypothesis test is proposed.