Statistical Science

Bayesian Animal Survival Estimation

S. P. Brooks, E. A. Catchpole, and B. J. T. Morgan

Full-text: Open access


We present the Bayesian approach to estimating parameters associated with animal survival on the basis of data arising from mark recovery and recapture studies. We provide two examples, beginning with a discussion of band-return models and examining data gathered from observations of blue winged teal (Aas discors), ringed as nestlings. We then look at open population recapture models, focusing on the Cormack- Jolly-Seber model, and examine this model in the context of a data set on European dippers (Cinclus cinclus). The Bayesian procedures are shown to be straightforward and provide a convenient framework for model-averaging, which incorporates the uncertainty due to model selection into the inference process. Sufficient detail is provided so that readers who wish to employ the Bayesian approach in this field can do so with ease. An example of BUGS code is also provided.

Article information

Statist. Sci. Volume 15, Number 4 (2000), 357-376.

First available in Project Euclid: 24 December 2001

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)


Brooks, S. P.; Catchpole, E. A.; Morgan, B. J. T. Bayesian Animal Survival Estimation. Statist. Sci. 15 (2000), no. 4, 357--376. doi:10.1214/ss/1009213003.

Export citation


  • Bayarri, M. J. and Berger, J. O. (1999). Quantifying surprise in the data and model verification. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 53-82. Oxford Univ. Press.
  • Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems. Statist. Sci. 10 3-66.
  • Bishop, Y. M. M., Fienberg, S. E. and Holland, P. W. (1975). Discrete Multivariate Analysis: Theory and Practice. MIT Press.
  • Bolfarine, H., Leite, J. G. and Rodriguez, J. (1992). On the estimation of the size of a finite and closed population. Biometrical J. 34 577-593.
  • Brooks, S. P. (1997). Markov chain Monte Carlo method and its application. Statistician 47 69-100.
  • Brooks, S. P. (1999). Bayesian analysis of animal abundance data via MCMC. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 723-731. Oxford Univ. Press.
  • Brooks, S. P., Catchpole, E. A. and Morgan, B. J. T. (2000). On the Bayesian analysis of ring-recovery data. Biometrics 56(3). To appear.
  • Brooks, S. P. and Gelman, A. (1998). Alternative methods for monitoring convergence of iterative simulation. J. Comp. Graphical Statist. 7 434-455.
  • Brooks, S. P. and Roberts, G. O. (1999). Assessing convergence of Markov chain Monte Carlo algorithms. Statist. Comput. 8 319-335. Brownie, C., Anderson, D. R., Burnham, K. P. and Robson,
  • D. S. (1985). Statistical inference from band recovery data: a handbook. Technical report, U.S. Dept. Interior, Fish and Wildlife Service.
  • Burnham, K. P. (1999). Random effects models in ringing and capture-recapture studies. Bird Study. Unpublished manuscript.
  • Carlin, B. P. and Louis, T. A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall, London.
  • Casella, G. and Robert, C. P. (1996). Rao-Blackwellization of sampling schemes. Biometrika 83 81-94.
  • Castledine, B. (1981). A Bayesian analysis of multiple capturerecapture sampling for a closed population. Biometrika 68 197-210.
  • Catchpole, E. A., Freeman, S. N. and Morgan, B. J. T. (1995). Modelling age variation in survival and reporting rates for recovery models. J. Appl. Statist. 22 597-609. Catchpole, E. A., Freeman, S. N., Morgan, B. J. T. and Harris,
  • M. P. (1998). Integrated recovery/recapture data analysis. Biometrics 54 33-46.
  • Catchpole, E. A. and Morgan, B. J. T. (1994). Boundary estimation in ring recovery models. J. Roy. Statist. Soc. Ser. B 56 385-391.
  • Catchpole, E. A. and Morgan, B. J. T. (1996). Model selection in ring recovery models using score tests. Biometrics 52 664- 672. Catchpole, E. A., Morgan, B. J. T., Freeman, S. N., Albon,
  • S. D. and Coulson, T. N. (1998). An integrated analysis of Soay sheep survival data. Technical Report UKC/IMS/98/32, Univ. Kent, Canterbury, England.
  • Cormack, R. M. (1992). Interval estimation for mark-recapture studies of closed populations. Biometrics 48 567-576.
  • Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Amer. Statist. Assoc. 91 883-904.
  • Dupuis, J. A. (1995). Bayesian estimation of movement and survival probabilities from capture-recapture data. Biometrika 82 761-772.
  • Freeman, M. F. and Tukey, J. W. (1950). Transformations related to the angular and square root. Ann. Math. Statist. 21 607-611.
  • Freeman, S. N. (1990). Statistical analysis of avian breeding and survival. Ph.D. thesis, Univ. Kent.
  • Freeman, S. N. and Morgan, B. J. T. (1992). A modeling strategy for recovery data from birds ringed as nestlings. Biometrics 48 217-235.
  • Gamerman, D. (1997). Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman and Hall, London.
  • Garthwaite, P. H., Yu, K. and Hope, P. B. (1995). Bayesian analysis of a multiple-recapture model. Comm. Statist. 24 2229-2247.
  • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (1995). Bayesian Data Analysis. Chapman and Hall, London.
  • Gelman, A., Meng, X. L. and Stern, H. (1996). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statist. Sinica 6 733-759.
  • George, E. L. and Robert, C. P. (1992). Capture-recapture estimation via Gibbs sampling. Biometrika 79 677-683.
  • Gilks, W. R., Thomas, D. and Spiegelhalter, D. J. (1992). Software for the Gibbs sampler. Comput. Sci. Statist. 24 439- 448.
  • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732.
  • Janz, R. J. (1980). Prior knowledge and ornithology. In Statist. Ornithology (B. J. T. Morgan and P. M. North, eds.) 303-310. Springer, Berlin.
  • Kadane, J. B. and Wolfson, L. J. (1998). Experiences in elicitation. Statistician 47 3-20.
  • Kass, R. E., Carlin, B. P., Gelman, A. and Neal, R. M. (1998). Markov chain Monte Carlo in practice: a roundtable discussion. Amer. Statist. 52 93-100.
  • Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773-795. Lebreton, J.-D., Burnham, K. P., Clobert, J. and Ander
  • son, D. R. (1992). Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs 62 67-118. Lebreton, J.-D., Morgan, B. J. T., Pradel, R. and Free
  • man, S. N. (1995). A simultaneous survival rate analysis of dead recovery and live recapture data. Biometrics 51 1418-1428.
  • Lee, S. M. and Chen, C. W. S. (2000). Bayesian inference of population size for behavioral response models. Statist. Sinica. To appear.
  • Link, W. and Cam, E. (1999). Of BUGS and birds: an introduction to Markov chain Monte Carlo. Unpublished manuscript.
  • Madigan, D. and York, J. C. (1997). Bayesian methods for estimation of the size of a closed population. Biometrika 84 19- 31.
  • Morgan, B. J. T. and Freeman, S. N. (1989). A model with firstyear variation for ring-recovery data. Biometrics 45 1087- 1101.
  • O'Hagan, A. O. (1998). Eliciting expert beliefs in substantial practical applications. Statistician 47 21-36.
  • Ripley, B. D. (1987). Stochastic Simulation. Wiley, NewYork.
  • Rubin, D. B. (1992). Using the SIR algorithm to simulate posterior distributions. In Bayesian Statistics 3 (J. M. Bernardo, M. M. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 395- 402. Oxford Univ. Press.
  • Schwarz, C. J. and Seber, G. A. F. (1999). Reviewof "Estimating Animal Abundance III." Statist. Sci. 14 427-456.
  • Spiegelhalter, D. J., Thomas, A. and Best, N. G. (1996). Computation on Bayesian graphical models. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 407-425. Oxford Univ. Press. Spiegelhalter, D. J., Thomas, A., Best, N. G. and Gilks, W.
  • R. (1996). BUGS: Bayesian Inference using Gibbs Sampling. Version 0.50. MRC Biostatistics Unit, Cambridge.
  • Tanner, M. and Wong, W. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-550.
  • Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701-1762.
  • Underhill, L. G. (1990). Bayesian estimation of the size of a closed population. Ring 13 235-254.
  • Vounatsou, P. and Smith, A. F. M. (1995). Bayesian analysis of ring-recovery data via Markov chain Monte Carlo simulation. Biometrics 51 687-708.
  • Wakefield, J. C., Gelfand, A. E. and Smith, A. F. M. (1991). Efficient generation of random variates via the ratio-ofuniforms method. Statist. Comput. 1 129-133.
  • White, G. C. and Burnham, K. P. (1999). Program MARK: survival estimation from populations of marked animals. Bird Study 46 (suppl.) 120-139.