Source: Braz. J. Probab. Stat.
Volume 23, Number 1
Capture–recapture methods are largely used for estimating the size of some cetacean populations. The application of those methods for photo-identification data of recognizable individuals is very common. Poor quality photographs may lead the analyst to identify two sightings of the same individual as being different (false-negative errors). This kind of matching error inflates population size estimates. We develop a Bayesian approach to obtain bias corrected estimates of the population size N. The method can be used for Mt type capture–recapture models (Otis et al. Wildlife Monographs 62 (1978) 1–135) involving two or more sampling occasions. We used the methodology for simulated data.
Darroch, J. H. (1958). The multiple-recapture census. I: Estimation of a closed population., Biometrika 45 343–359.
Mathematical Reviews (MathSciNet): MR119360
da-Silva, C. Q., Rodrigues, J., Leite, J. G. and Milan, L. A. (2003). Bayesian estimation of the size of a closed population using photo-id data with part of the population uncatchable., Communications in Statistics. Simulation and Computation 32 677–696.
Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion)., Statistical Science 7 457–511.
Givens, G. H., Smith, D. D. and Tweedie, R. L. (1997). Publication bias in meta-analysis: A Bayesian data-augmentation approach to account for issues exemplified in the passive smoking debate., Statistical Science 12 221–250.
Heitjan, D. F. and Landis, J. R. (1994). Assessing secular trends in blood pressure: A multiple-imputation approach., Journal of the American Statistical Association 89 427, 750–759.
Otis, D. L., Burnham, K. P., White, G. C. and Anderson, D. R. (1978). Statistical inference from capture data on closed animal populations., Wildlife Monographs 62 1–135.
Rubin, D. B. and Schenker, N. (1986). Multiple imputation from simple random samples with ignorable nonresponse., Journal of the American Statistical Association 81 366–374.
Mathematical Reviews (MathSciNet): MR845877
Schafer, J. L. (1997)., Analysis of Incomplete Multivariate Data. Chapman & Hall, New York.
Smith, P. J. (1991). Bayesian analysis of multiple capture–recapture model., Biometrika 78 399–401.
Stevick, P. T., Palsboll, P. J. and Allen, J. M. (1998). Comparison of capture–recapture results using photographic and genetic identification: Relative rates and sources of errors. WMMSC, Monaco. Abstract, volume.
Stevick, P. T., Palsboll, P. J., Smith, T. D., Bravington, M. V. and Hammond, P. S. (2001). Errors in identification using natural markings: Rates, sources, and effects on capture–recapture estimates of abundances., Canadian Journal of Fisheries and Aquatic Sciences 58 1861–1870.
Tanner, M. A. and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation., Journal of the American Statistical Association 82 528–550.
Mathematical Reviews (MathSciNet): MR898357