Abstract
We propose an analytical solution to the on-off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a consistent way.
We use a large enough family of prior distributions of relevant parameters. The proposed analysis is designed to provide Bayesian solutions that can be used for any number of observed on-off events, including zero.
The procedure is checked using Monte Carlo simulations. The usefulness of the method is demonstrated on examples from gamma-ray astronomy