UNIFIED APPROACH TO THE CLASSICAL STATISTICAL-ANALYSIS OF SMALL SIGNALS

We give a classical confidence belt construction which unifies the tre atment of upper confidence limits for null results and two-sided confi dence intervals for non-null results. The unified treatment solves a p roblem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confide nce intervals if the choice is based on the data. We apply the constru ction to two related problems which have recently been a battleground between classical and Bayesian statistics: Poisson processes with back ground and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construct ion avoids unphysical confidence intervals. In contrast with some popu lar Bayesian intervals, our intervals eliminate conservatism (frequent ist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experime nts searching for neutrino oscillations. We show that this technique b oth gives correct coverage and is powerful, while other classical tech niques that have been used by neutrino oscillation search experiments fail one or both of these criteria. [S0556-2821(98)00109-X].