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

Approximation intensity for pairwise interaction Gibbs point processes using determinantal point processes