## Electronic Journal of Statistics

### Fast approximation of the intensity of Gibbs point processes

#### 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

https://projecteuclid.org/euclid.ejs/1340974139

Digital Object Identifier
doi:10.1214/12-EJS707

Mathematical Reviews number (MathSciNet)
MR2988442

Zentralblatt MATH identifier
1268.60063

#### 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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