IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i2d10.1007_s11009-019-09741-5.html
   My bibliography  Save this article

Computation of Coverage Probabilities in a Spherical Germ-Grain Model

Author

Listed:
  • Ian Flint

    (Nanyang Technological University)

  • Nicolas Privault

    (Nanyang Technological University)

Abstract

We consider a spherical germ-grain model on ℝ d $\mathbb {R}^{d}$ in which the centers of the spheres are driven by a possibly non-Poissonian point process. We show that various covering probabilities can be expressed using the cumulative distribution function of the random radii on one hand, and distances to certain subsets of ℝ d $\mathbb {R}^{d}$ on the other hand. This result allows us to compute the spherical and linear contact distribution functions, and to derive expressions which are suitable for numerical computation. Determinantal point processes are an important class of examples for which the relevant quantities take the form of Fredholm determinants.

Suggested Citation

  • Ian Flint & Nicolas Privault, 2021. "Computation of Coverage Probabilities in a Spherical Germ-Grain Model," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 491-502, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09741-5
    DOI: 10.1007/s11009-019-09741-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09741-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-019-09741-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Frédéric Lavancier & Jesper Møller & Ege Rubak, 2015. "Determinantal point process models and statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 853-877, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. José J. Quinlan & Fernando A. Quintana & Garritt L. Page, 2021. "On a class of repulsive mixture models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 445-461, June.
    2. Christophe Ange Napoléon Biscio & Frédéric Lavancier, 2017. "Contrast Estimation for Parametric Stationary Determinantal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 204-229, March.
    3. Frédéric Lavancier & Jesper Møller, 2016. "Modelling Aggregation on the Large Scale and Regularity on the Small Scale in Spatial Point Pattern Datasets," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 587-609, June.
    4. Zhenchong Mo & Lin Gong & Mingren Zhu & Junde Lan, 2024. "The Generative Generic-Field Design Method Based on Design Cognition and Knowledge Reasoning," Sustainability, MDPI, vol. 16(22), pages 1-34, November.
    5. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    6. Jean-François Coeurjolly & Jesper Møller & Rasmus Waagepetersen, 2017. "A Tutorial on Palm Distributions for Spatial Point Processes," International Statistical Review, International Statistical Institute, vol. 85(3), pages 404-420, December.
    7. Subhroshekhar Ghosh & Soumendu Sundar Mukherjee, 2022. "Learning with latent group sparsity via heat flow dynamics on networks," Papers 2201.08326, arXiv.org.
    8. Frédéric Lavancier & Arnaud Poinas & Rasmus Waagepetersen, 2021. "Adaptive estimating function inference for nonstationary determinantal point processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 87-107, March.
    9. Chong Deng & Yongtao Guan & Rasmus P. Waagepetersen & Jingfei Zhang, 2017. "Second‐order quasi‐likelihood for spatial point processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1311-1320, December.
    10. Poinas, Arnaud, 2019. "A bound of the β-mixing coefficient for point processes in terms of their intensity functions," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 88-93.
    11. Jesper Møller & Ninna Vihrs, 2022. "Should We Condition on the Number of Points When Modelling Spatial Point Patterns?," International Statistical Review, International Statistical Institute, vol. 90(3), pages 551-562, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09741-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.