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Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

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  • Jesper Møller
  • Håkon Toftaker

Abstract

type="main" xml:id="sjos12041-abs-0001"> We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.

Suggested Citation

  • Jesper Møller & Håkon Toftaker, 2014. "Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 414-435, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:414-435
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    File URL: http://hdl.handle.net/10.1111/sjos.12041
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    References listed on IDEAS

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    1. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. Grabarnik, Pavel & Myllymäki, Mari & Stoyan, Dietrich, 2011. "Correct testing of mark independence for marked point patterns," Ecological Modelling, Elsevier, vol. 222(23), pages 3888-3894.
    4. Mugglestone, Moira A. & Renshaw, Eric, 1996. "A practical guide to the spectral analysis of spatial point processes," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 43-65, January.
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    1. Nicoletta D’Angelo & Marianna Siino & Antonino D’Alessandro & Giada Adelfio, 2022. "Local spatial log-Gaussian Cox processes for seismic data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 633-671, December.
    2. María P. Frías & Antoni Torres-Signes & María D. Ruiz-Medina & Jorge Mateu, 2022. "Spatial Cox processes in an infinite-dimensional framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 175-203, March.

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