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2012 Fast approximation of the intensity of Gibbs point processes
Adrian Baddeley, Gopalan Nair
Electron. J. Statist. 6: 1155-1169 (2012). DOI: 10.1214/12-EJS707


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.


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Adrian Baddeley. Gopalan Nair. "Fast approximation of the intensity of Gibbs point processes." Electron. J. Statist. 6 1155 - 1169, 2012.


Published: 2012
First available in Project Euclid: 29 June 2012

zbMATH: 1268.60063
MathSciNet: MR2988442
Digital Object Identifier: 10.1214/12-EJS707

Primary: 60G55
Secondary: 62E17 , 82B21

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

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society


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