M ar 1 99 7 Signal Confidence Limits from a Neural Network Data Analysis

Let N experimental data be given, such that N = Ns + Nb, (Ns ≪ Nb), where Ns is the number of signals, Nb the number of background events, and both are unknown. Assume that a neural network (NN) has been trained, such that it will tag signals with efficiency Fs and background data with Fb, (1 > Fs ≫ Fb > 0). Applying the NN yields N Y < N tagged events. From the knowledge of N we find the a-posteriori likelihood P (Ns) that there are actually Ns signals in the data set. Once P (Ns) is given, confidence limits for the signal probability follow. Subsequently, we compare our results with those obtained by starting off with a maximum entropy type of assumption for the a-priori likelihood that there are Ns signals in the data. Certain difficulties are encountered in the latter case. This research was partially funded by the Department of Energy under contract DE-FG05-87ER40319 and by the Austrian Ministry of Science. Department of Physics, The Florida State University, Tallahassee, FL 32306, USA. Supercomputer Computations Research Institute, Tallahassee, FL 32306, USA. E-mail: [email protected] Institut für Kernphysik, Technische Universität Wien, A-1040 Vienna, Austria E-mail: [email protected]