An ABC method for posterior sampling of marked point processes

This paper presents an ABC algorithm, called ABC Shadow, that can be applied to sample marked point processes posterior densities. The proposed method uses the ideas given by the auxiliary variable Metropolis-Hastings of (M{\o}ller et al., 2006). The obtained algorithm solves the main condition to be fulfilled by any ABC algorithm, in order to be useful in practice. This condition requires enough samples in the parameter space region, induced by the observed statistics (Blum, 2010). The algorithm is tested on entirely known exponential family models and on two point processes, the Strauss and the Candy models.