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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

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.

Citation

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Adrian Baddeley. Gopalan Nair. "Fast approximation of the intensity of Gibbs point processes." Electron. J. Statist. 6 1155 - 1169, 2012. https://doi.org/10.1214/12-EJS707

Information

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

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

Subjects:
Primary: 60G55
Secondary: 62E17, 82B21

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

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