  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.
