[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/bpj/ijbist/v13y2017i1p24n3.html
   My bibliography  Save this article

Parameter Estimation of a Two-Colored Urn Model Class

Author

Listed:
  • Chloé Le Goff Line

    (Department of Mathematics, Uppsala Universitet, Uppsala, Sweden)

  • Soulier Philippe

    (Department of Mathematics, Universite Paris-Nanterre, Nanterre, le-de-France, France)

Abstract
Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw a ball at each step depends on the number of balls of each color and on a multidimensional parameter through a function, called choice function. We introduce two estimators of the parameter: the maximum likelihood estimator and a weighted least squares estimator which is less efficient, but is closer to the calibration techniques used in the applied literature. In general, the model is an inhomogeneous Markov chain and this property makes the estimation of the parameter impossible on a single path, even if it were infinite. Therefore we assume that we observe i.i.d. experiments, each of a predetermined finite length. This is coherent with the usual experimental set-ups. We apply the statistical framework to a real life experiment: the selection of a path among pre-existing channels by an ant colony. We performed experiments, which consisted of letting ants pass through the branches of a fork. We consider the particular urn model proposed by J.-L. Deneubourg et al. in 1990 to describe this phenomenon. We simulate this model for several parameter values in order to assess the accuracy of the MLE and the WLSE. Then we estimate the parameter from the experimental data and evaluate confident regions with Bootstrap algorithms. The findings of this paper do not contradict the biological literature, but give statistical significance to the values of the parameter found therein.

Suggested Citation

  • Chloé Le Goff Line & Soulier Philippe, 2017. "Parameter Estimation of a Two-Colored Urn Model Class," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-24, May.
    • Handle: RePEc:bpj:ijbist:v:13:y:2017:i:1:p:24:n:3
    DOI: 10.1515/ijb-2016-0029
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/ijb-2016-0029
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/ijb-2016-0029?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. S. Nicolis & A. Dussutour, 2008. "Self-organization, collective decision making and resource exploitation strategies in social insects," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 379-385, October.
    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. Dussutour, Audrey & Nicolis, Stamatios C., 2013. "Flexibility in collective decision-making by ant colonies: Tracking food across space and time," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 32-38.
    2. Natalia Zabzina & Audrey Dussutour & Richard P Mann & David J T Sumpter & Stamatios C Nicolis, 2014. "Symmetry Restoring Bifurcation in Collective Decision-Making," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-11, 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:bpj:ijbist:v:13:y:2017:i:1:p:24:n:3. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.