Signal discovery in sparse spectra:: A Bayesian analysis

A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and, in particular, applicable to sparsely populated spectra. Monte Carlo techniques to evaluate the sensitivity of an experiment are described. As an example, the method is used to calculate the sensitivity of the GERDA experiment to neutrinoless double beta decay.