Electronic Journal of Statistics

Fast approximation of the intensity of Gibbs point processes

Adrian Baddeley and Gopalan Nair

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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

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

First available in Project Euclid: 29 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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