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Testing for Spatial Association between a Point Process and Another Stochastic Process

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  • Mark Berman

Abstract

Motivated by a problem in geology, this paper proposes some tests of the spatial association between a point process and some other stochastic process of geometric structures, G. All the tests are performed conditionally on the realization of G. Under the null hypothesis that the point process is a stationary Poisson process independent of G, some of these statistics have well‐known distributional properties, even in small samples. The Poisson assumption is relaxed using a conditional Monte Carlo test suggested by Lotwick and Silverman (1982). The tests are applied to a geological data set.

Suggested Citation

  • Mark Berman, 1986. "Testing for Spatial Association between a Point Process and Another Stochastic Process," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(1), pages 54-62, March.
    • Handle: RePEc:bla:jorssc:v:35:y:1986:i:1:p:54-62
    DOI: 10.2307/2347865
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    1. repec:jss:jstsof:12:i06 is not listed on IDEAS
    2. 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.
    3. Jiří Dvořák & Tomáš Mrkvička & Jorge Mateu & Jonatan A. González, 2022. "Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 90(3), pages 592-621, December.
    4. Laura Anton-Sanchez & Pedro Larrañaga & Ruth Benavides-Piccione & Isabel Fernaud-Espinosa & Javier DeFelipe & Concha Bielza, 2017. "Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    5. Nicolás Younes Cárdenas & Estefanía Erazo Mera, 2016. "Landslide susceptibility analysis using remote sensing and GIS in the western Ecuadorian Andes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(3), pages 1829-1859, April.
    6. Nicoletta D’Angelo & Giada Adelfio, 2024. "Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes," Statistical Papers, Springer, vol. 65(6), pages 3651-3679, August.
    7. Yan Zhu & Stephan Getzin & Thorsten Wiegand & Haibao Ren & Keping Ma, 2013. "The Relative Importance of Janzen-Connell Effects in Influencing the Spatial Patterns at the Gutianshan Subtropical Forest," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-8, September.
    8. Lister, Andrew J. & Leites, Laura P., 2018. "Modeling and simulation of tree spatial patterns in an oak-hickory forest with a modular, hierarchical spatial point process framework," Ecological Modelling, Elsevier, vol. 378(C), pages 37-45.
    9. Guangshun Bai & Xuemei Yang & Guangxin Bai & Zhigang Kong & Jieyong Zhu & Shitao Zhang, 2024. "Examining the Controls on the Spatial Distribution of Landslides Triggered by the 2008 Wenchuan Ms 8.0 Earthquake, China, Using Methods of Spatial Point Pattern Analysis," Sustainability, MDPI, vol. 16(16), pages 1-24, August.
    10. Xinyu Zhou & Wei Wu, 2024. "Statistical Depth in Spatial Point Process," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    11. Denis Allard & Anders Brix & Joël Chadoeuf, 2001. "Testing Local Independence between Two Point Processes," Biometrics, The International Biometric Society, vol. 57(2), pages 508-517, June.

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