The search of gamma-ray sources in the extra-galactic space is one of the main targets of the Fermi telescope project, which aims to identify and study the nature of high energy phenomena in the universe. This requires to separate their signal from the diffuse gamma-ray background, an isotropic contamination of the entire area observed by the telescope.

Starting from a collection of photons, we performed an unsupervised analysis using a Bayesian mixture model with an unknown number of components to determine the number of gamma ray sources in the map, their intensities and their coordinates in the sky.

The parameters of the model were estimated using a reversible jump MCMC algorithm, which implements four different types of moves to take into account that the dimension of the parametric space is not fixed.

We finally propose a new method to qualify the nature of each detected cluster. This method exploits the distributions of both the weights of the mixture components and the energy spectra, which result after all particles were allocated into the discovered groups.