Electronic Journal of Statistics

Fast approximation of the intensity of Gibbs point processes

Adrian Baddeley and Gopalan Nair

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Abstract

The intensity of a Gibbs point process model is usually an intractable function of the model parameters. This is a severe restriction on the practical application of such models. We develop a new approximation for the intensity of a stationary Gibbs point process on $\mathbb{R}^{d}$. For pairwise interaction processes, the approximation can be computed rapidly and is surprisingly accurate. The new approximation is qualitatively similar to the mean field approximation, but is far more accurate, and does not exhibit the same pathologies. It may be regarded as a counterpart of the Percus-Yevick approximation.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1155-1169.

Dates
First available in Project Euclid: 29 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1340974139

Digital Object Identifier
doi:10.1214/12-EJS707

Mathematical Reviews number (MathSciNet)
MR2988442

Zentralblatt MATH identifier
1268.60063

Subjects
Primary: 60G55: Point processes
Secondary: 82B21: Continuum models (systems of particles, etc.) 62E17: Approximations to distributions (nonasymptotic)

Keywords
Georgii-Nguyen-Zessin formula Gibbs point process Lambert $W$ function mean field approximation pairwise interaction point process Palm distribution Papangelou conditional intensity Percus-Yevick approximation Poisson approximation Poisson-saddlepoint approximation Strauss process

Citation

Baddeley, Adrian; Nair, Gopalan. Fast approximation of the intensity of Gibbs point processes. Electron. J. Statist. 6 (2012), 1155--1169. doi:10.1214/12-EJS707. https://projecteuclid.org/euclid.ejs/1340974139


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