IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v69y2001i1p81-104.html
   My bibliography  Save this article

Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns

Author

Listed:
  • Jorge Mateu
  • Francisco Montes

Abstract

Several authors have proposed stochastic and non‐stochastic approximations to the maximum likelihood estimate (MLE) for Gibbs point processes in modelling spatial point patterns with pairwise interactions. The approximations are necessary because of the difficulty of evaluating the normalizing constant. In this paper, we first provide a review of methods which yield crude approximations to the MLE. We also review methods based on Markov chain Monte Carlo techniques for which exact MLE has become feasible. We then present a comparative simulation study of the performance of such methods of estimation based on two simulation techniques, the Gibbs sampler and the Metropolis‐Hastings algorithm, carried out for the Strauss model.

Suggested Citation

  • Jorge Mateu & Francisco Montes, 2001. "Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 69(1), pages 81-104, April.
    • Handle: RePEc:bla:istatr:v:69:y:2001:i:1:p:81-104
    DOI: 10.1111/j.1751-5823.2001.tb00481.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1751-5823.2001.tb00481.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1751-5823.2001.tb00481.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. Vinayak Rao & Ryan P. Adams & David D. Dunson, 2017. "Bayesian inference for Matérn repulsive processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 877-897, June.
    2. Jorge Mateu & Francisco Montes, 2001. "Pseudo-likelihood Inference for Gibbs Processes with Exponential Families through Generalized Linear Models," Statistical Inference for Stochastic Processes, Springer, vol. 4(2), pages 125-154, May.
    3. Matthew Bognar, 2008. "Bayesian modeling of continuously marked spatial point patterns," Computational Statistics, Springer, vol. 23(3), pages 361-379, July.
    4. Bognar, Matthew A., 2005. "Bayesian inference for spatially inhomogeneous pairwise interacting point processes," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 1-18, April.

    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:istatr:v:69:y:2001:i:1:p:81-104. 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: https://edirc.repec.org/data/isiiinl.html .

    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.