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Objective Bayesian analysis for a capture–recapture model

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  • Chang Xu
  • Dongchu Sun
  • Chong He

Abstract

In this paper, we study a special capture–recapture model, the $$M_t$$ M t model, using objective Bayesian methods. The challenge is to find a justified objective prior for an unknown population size $$N$$ N . We develop an asymptotic objective prior for the discrete parameter $$N$$ N and the Jeffreys’ prior for the capture probabilities $$\varvec{\theta }$$ θ . Simulation studies are conducted and the results show that the reference prior has advantages over ad-hoc non-informative priors. In the end, two real data examples are presented. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Chang Xu & Dongchu Sun & Chong He, 2014. "Objective Bayesian analysis for a capture–recapture model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 245-278, April.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:245-278
    DOI: 10.1007/s10463-013-0413-1
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    References listed on IDEAS

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    1. Alessio Farcomeni & Luca Tardella, 2010. "Reference Bayesian methods for recapture models with heterogeneity," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 187-208, May.
    2. James O. Berger & Jose M. Bernardo & Dongchu Sun, 2012. "Objective Priors for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 636-648, June.
    3. Adrian E. Raftery, 1988. "Analysis of a Simple Debugging Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 12-22, March.
    4. Luca Tardella, 2002. "A new Bayesian method for nonparametric capture-recapture models in presence of heterogeneity," Biometrika, Biometrika Trust, vol. 89(4), pages 807-817, December.
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