IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v37y2010i3p365-381.html
   My bibliography  Save this article

Likelihood Inference for Unions of Interacting Discs

Author

Listed:
  • JESPER MØLLER
  • KATEŘINA HELISOVÁ

Abstract

. This is probably the first paper which discusses likelihood inference for a random set using a germ‐grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation‐based maximum likelihood inference and the effect of specifying different reference Poisson models.

Suggested Citation

  • Jesper Møller & Kateřina Helisová, 2010. "Likelihood Inference for Unions of Interacting Discs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 365-381, September.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:3:p:365-381
    DOI: 10.1111/j.1467-9469.2009.00660.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2009.00660.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2009.00660.x?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kateřina Staňková Helisová & Jakub Staněk, 2014. "Dimension Reduction in Extended Quermass-Interaction Process," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 355-368, June.
    2. Viktor Beneš & Jakub Večeřa & Milan Pultar, 2019. "Planar Segment Processes with Reference Mark Distributions, Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 683-698, September.
    3. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    4. Vesna Gotovac Dogaš & Kateřina Helisová, 2021. "Testing Equality of Distributions of Random Convex Compact Sets via Theory of 𝕹 $\mathfrak {N}$ -Distances," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 503-526, June.
    5. Athanasios C. Micheas & Jiaxun Chen, 2018. "sppmix: Poisson point process modeling using normal mixture models," Computational Statistics, Springer, vol. 33(4), pages 1767-1798, December.
    6. Johan Debayle & Vesna Gotovac Ðogaš & Kateřina Helisová & Jakub Staněk & Markéta Zikmundová, 2021. "Assessing Similarity of Random sets via Skeletons," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 471-490, June.
    7. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2014. "On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 451-463, June.

    More about this item

    Statistics

    Access and download statistics

    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:bla:scjsta:v:37:y:2010:i:3:p:365-381. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.