Signal confidence limits from a neural network data analysis Original Research Article

This paper deals with a situation of some importance for the analysis of experimental data via Neural Network (NN) or similar devices: Let N data be given, such that N = Ns + Nb, where Ns is the number of signals, Nb the number of background events, and both are unknown. Assume that a NN has been trained, such that it will tag signals with efficiency Fs (0 < Fs < 1) and background data with Fb (0 < Fb < 1). Applying the NN yields NY tagged events. We demonstrate that the knowledge of NY is sufficient to calculate confidence bounds for the signal likelihood, which have the same statistical interpretation as the Clopper-Pearson bounds for the well-studied case of direct signal observation. Subsequently, we discuss rigorous bounds for the a posteriori distribution function of the signal probability, as well as for the (closely related) likelihood that there are Ns signals in the data. We compare them with results obtained by starting off with a maximum entropy type assumption for the a priori likelihood that there are Ns signals in the data and applying the Bayesian theo