Electronic Journal of Statistics

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

Jean-François Coeurjolly and Frédéric Lavancier

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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.

Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 3181-3203.

Dates
Received: December 2017
First available in Project Euclid: 27 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1538013687

Digital Object Identifier
doi:10.1214/18-EJS1477

Subjects
Primary: 60G55: Point processes
Secondary: 82B21: Continuum models (systems of particles, etc.)

Keywords
Determinantal point process Georgii-Nguyen-Zessin formula Gibbs point process Laplace transform

Rights
Creative Commons Attribution 4.0 International License.

Citation

Coeurjolly, Jean-François; Lavancier, Frédéric. Intensity approximation for pairwise interaction Gibbs point processes using determinantal point processes. Electron. J. Statist. 12 (2018), no. 2, 3181--3203. doi:10.1214/18-EJS1477. https://projecteuclid.org/euclid.ejs/1538013687


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References

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