Unbiased cut selection for optimal upper limits in neutrino detectors: the model rejection potential technique

We present a method for optimising experimental cuts in order to place the strongest constraints (upper limits) on theoretical signal models. The method relies only on signal and background expectations derived from Monte-Carlo simulations, so no bias is introduced by looking at actual data, for instance by setting a limit based on expected signal above the ``last remaining data event.'' After discussing the concept of the ``average upper limit,'' based on the expectation from an ensemble of repeated experiments with no true signal, we show how the best model rejection potential is achieved by optimising the cuts to minimise the ratio of this ``average upper limit'' to the expected signal from the model. As an example, we use this technique to determine the limit sensitivity of kilometre scale neutrino detectors to extra-terrestrial neutrino fluxes from a variety of models, e.g. active galaxies and gamma-ray bursts. We suggest that these model rejection potential optimised limits be used as a standard method of comparing the sensitivity of proposed neutrino detectors.