uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Parameter Estimation of a Two-Colored Urn Model Class
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Univ Paris Nanterre, Dept Math, Nanterre, Le De France, France..
2017 (English)In: INTERNATIONAL JOURNAL OF BIOSTATISTICS, ISSN 2194-573X, Vol. 13, no 1, 20160029Article in journal (Refereed) Published
Abstract [en]

Though widely used in applications, reinforced randomwalk 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.

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH , 2017. Vol. 13, no 1, 20160029
Keyword [en]
ant behavior, asymptotic proprieties of estimators, Deneubourg's choice function, reinforced random walk parameter estimation, urn model parameter estimation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-333413DOI: 10.1515/ijb-2016-0029ISI: 000406656700014OAI: oai:DiVA.org:uu-333413DiVA: diva2:1157113
Available from: 2017-11-15 Created: 2017-11-15 Last updated: 2017-11-15Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text
By organisation
Department of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 20 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf