Discovering and Locating High-Energy Extra-galactic Sources by Bayesian Mixture Modelling

Discovering and locating gamma-ray sources in the whole sky map is a declared target of the Fermi Gamma-ray Space Telescope collaboration. In this paper, we carry out an unsupervised analysis of the collection of high-energy photons accumulated by the Large Area Telescope, the principal instrument on board the Fermi spacecraft, over a period of around 7.5 years using a Bayesian mixture model. A fixed, though unknown, number of parametric components identify the extra-galactic emitting sources we are searching for, while a further component represents parametrically the diffuse gamma-ray background due to both, extra-galactic and galactic high-energy photon emission. We determine the number of sources, their coordinates on the map and their intensities. The model parameters are estimated using a reversible jump MCMC algorithm which implements four different types of moves. These allow us to explore the dimension of the parameter space. The possible transitions remove from or add a source to the model, while leaving the background component unchanged. We furthermore present an heuristic procedure, based on the posterior distribution of the mixture weights, to qualify the nature of each detected source.