Intensity approximation for pairwise interaction Gibbs point processes using determinantal point processes

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 (2012) developped the Poisson-saddlepoint app...

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Bibliographic Details
Published in:Electronic journal of statistics 2018-01, Vol.12 (2), p.3181-3203
Main Authors: Coeurjolly, Jean-François, Lavancier, Frédéric
Format: Article
Language:English
Subjects:
Methodology
Statistics
Statistics Theory
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Summary: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 (2012) 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 determinan-tal 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.
ISSN:1935-7524
1935-7524
DOI:10.1214/18-EJS1477