  The intensity of a Gibbs point process is usually an intractable function of
the model parameters. For repulsive pairwise interaction point processes, this
intensity can be expressed as the Laplace transform of some particular
function. Baddeley and Nair (2002) developped the Poisson-saddlepoint
approximation which consists, for basic models, in calculating this Laplace
transform with respect to a homogeneous Poisson point process. In this paper,
we develop an approximation which consists in calculating the same Laplace
transform with respect to a specific determinantal point process. This new
approximation is efficiently implemented and turns out to be more accurate than
the Poisson-saddlepoint approximation, as demonstrated by some numerical
examples.
