Bayesian capture-recapture analysis and model selection allowing for heterogeneity and behavioral effects



In this article, we present Bayesian analysis of capture-recapture models for a closed population which allows for heterogeneity of capture probabilities between animals and bait/trap effects. We use a flexible discrete mixture model to account for the heterogeneity and behavioral effects. In addition we present a solid model selection criterion. Through illustrations with a motivating dataset, we demonstrate how Bayesian analysis can be applied in this setting and discuss some major benefits which result, including consideration of informative priors based on historical data.

Key Words

Bayesian inference Capture-recapture models Closed population Heterogeneity Gibbs sampling MCMC WinBUGS 


  1. Akaike, H. (1973), “Information Theory and an Extension of the Maximum Likelihood Principle,” in Proceedings of the Second International Symposium on Information Theory, eds. B. N. Petrov and F. Csaki, Budapest: Akademiai Kiado, pp. 267–281.Google Scholar
  2. Basu, S., and Ebrahimi, N. (2001), “Bayesian Capture-Recapture Methods for Error Detection and Estimation of Population Size: Heterogeneity and Dependence,” Biometrika, 88, 269–279.MATHCrossRefMathSciNetGoogle Scholar
  3. Berger, J. O. (1985), Statistical Decision Theory and Bayesian Analysis (2nd ed.), New York: Springer-Verlag.MATHGoogle Scholar
  4. Brownie, C., Anderson, D. R., Burnham, K. P., and Robson, D. S. (1985), Statistical Inference From Band Recovery Data: A Handbook (2nd ed.), Washington, DC: U.S. Fish and Wildlife Service Resources, Publication 156.Google Scholar
  5. Castledine, B. (1981), “Bayesian Analysis of Multiple-Recapture Sampling for a Closed Population,” Biometrika, 67, 197–210.CrossRefMathSciNetGoogle Scholar
  6. Darroch, J. N. (1958), “The Multiple Recapture Census. I: Estimation of a Closed Population,” Biometrika, 36, 343–359.MathSciNetGoogle Scholar
  7. Gelfand, A. E., and Ghosh, S. K. (1998), “Model Choice: A Minimum Posterior Loss Approach,” Biometrika, 85, 1–11.MATHCrossRefMathSciNetGoogle Scholar
  8. George, E. I., and Robert, C. P. (1992), “Capture-Recapture Estimation via Gibbs Sampling,” Biometrika, 79, 677–683.MATHMathSciNetGoogle Scholar
  9. Ishwaran, H., and Zarepour, M. (2002), “Dirichlet Prior Sieves in Finite Normal Mixtures,” Statistica Sinica, 12, 941–963.MATHMathSciNetGoogle Scholar
  10. Jeffreys, H. (1946), “An Invariant Form for the Prior Probability in Estimation Problems,” Proceedings of the Royal Statistical Society, Ser. A, 186, 453–461.MATHCrossRefMathSciNetGoogle Scholar
  11. Jolly, G. M. (1965), “Explicit Estimates From Capture-Recapture Data with Both Death and Immigration—Stochastic Model,” Biometrika, 52, 225–247.MATHMathSciNetGoogle Scholar
  12. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), New York: Chapman and Hall.MATHGoogle Scholar
  13. McLachlan, G., and Peel, D. (2000), Finite Mixture Models, New York: Wiley.MATHCrossRefGoogle Scholar
  14. Norris, J. L., and Pollock, K. H. (1995), “A Capture-Recapture Model with Heterogeneity and Behavioral Response,” Environmental and Ecological Statistics, 2, 305–313.CrossRefGoogle Scholar
  15. — (1996), “Nonparametric MLE Under Two Closed Capture-Recapture Models with Heterogeneity,” Biometrics, 52, 639–649.MATHCrossRefGoogle Scholar
  16. Otis, D. L., Burnham, K. P., White, G. C., and Anderson, D. R. (1978), “Statistical Inference From Capture Data on Closed Animal Population,” Wildlife Monographs, 62.Google Scholar
  17. Pledger, S. (2000), “Unified Maximum Likelihood Estimates for Closed Capture-Recapture Models Under Mixtures,” Biometrics, 56, 434–442.MATHCrossRefGoogle Scholar
  18. Schwartz, G. (1978), “Estimating the Dimension of a Model,” The Annal of Statistics, 6, 461–464.CrossRefGoogle Scholar
  19. Seber, G. A. F. (1965), “A Note on the Multiple-Recapture Census,” Biometrika, 52, 249–259.MATHMathSciNetGoogle Scholar
  20. Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. (2001), WinBUGS User Manual (version. 1.4), Cambridge, UK. MRC Biostatistics Unit. Available at Scholar
  21. Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and van der Linde, A. (2002), “Bayesian Measures of Model Complexity and Fit,” (with discussion), Journal of the Royal Statistical Society, Ser. B, 64, 583–639.MATHCrossRefGoogle Scholar
  22. Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985), Statistical Analysis of Finite Mixture Distributions, New York: Wiley.MATHGoogle Scholar

Copyright information

© International Biometric Society 2005

Authors and Affiliations

  1. 1.Department of StatisticsNorth Carolina State UniversityRaleigh
  2. 2.Department of MathematicsWake Forest UniversityWinston-Salem

Personalised recommendations