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2018 Intensity approximation for pairwise interaction Gibbs point processes using determinantal point processes
Jean-François Coeurjolly, Frédéric Lavancier
Electron. J. Statist. 12(2): 3181-3203 (2018). DOI: 10.1214/18-EJS1477

Abstract

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 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.

Citation

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Jean-François Coeurjolly. Frédéric Lavancier. "Intensity approximation for pairwise interaction Gibbs point processes using determinantal point processes." Electron. J. Statist. 12 (2) 3181 - 3203, 2018. https://doi.org/10.1214/18-EJS1477

Information

Received: 1 December 2017; Published: 2018
First available in Project Euclid: 27 September 2018

zbMATH: 06970001
MathSciNet: MR3858696
Digital Object Identifier: 10.1214/18-EJS1477

Subjects:
Primary: 60G55
Secondary: 82B21

JOURNAL ARTICLE
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Vol.12 • No. 2 • 2018
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