The intensity of a Gibbs point process is usually an intractable function of the model parameters. For pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function. A. Baddeley and G. Nair (2012) developped the Poisson-saddlepoint approximation which consists in calculating this Laplace transform with respect to a homogeneous Poisson point process. We suggest an alternative approximation which consists in calculating the same Laplace transform with respect to a determinantal point process. This new approximation, implemented in just one line code, turns out to be more accurate than the Poisson-saddlepoint approximation.
This is a joint work with J.-F. Coeurjolly.