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.

[1]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[2]  G. Jolly.  EXPLICIT ESTIMATES FROM CAPTURE-RECAPTURE DATA WITH BOTH DEATH AND IMMIGRATION-STOCHASTIC MODEL. , 1965, Biometrika.

[3]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[4]  B. J. Castledine.  A Bayesian analysis of multiple-recapture sampling for a closed population , 1981 .

[5]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[6]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[7]  David R. Anderson,et al.  Statistical inference from capture data on closed animal populations , 1980 .

[8]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[9]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[10]  J. Norris,et al.  NONPARAMETRIC MLE UNDER TWO CLOSED CAPTURE-RECAPTURE MODELS WITH HETEROGENEITY , 1996 .

[11]  N. Ebrahimi,et al.  Bayesian capture-recapture methods for error detection and estimation of population size: Heterogeneity and dependence , 2001 .

[12]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[13]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[14]  H. Ishwaran,et al.  DIRICHLET PRIOR SIEVES IN FINITE NORMAL MIXTURES , 2002 .

[15]  David J. Spiegelhalter,et al.  WinBUGS user manual version 1.4 , 2003 .

[16]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[17]  J. Darroch.  THE MULTIPLE-RECAPTURE CENSUS I. ESTIMATION OF A CLOSED POPULATION , 1958 .

[18]  Aki Vehtari.  Discussion to "Bayesian measures of model complexity and fit" by Spiegelhalter, D.J., Best, N.G., Carlin, B.P., and van der Linde, A. , 2002 .

[19]  Alan E. Gelfand,et al.  Model choice: A minimum posterior predictive loss approach , 1998, AISTATS.

[20]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[21]  S. Pledger.  Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures , 2000, Biometrics.

[22]  David R. Anderson,et al.  Statistical Inference from Band Recovery Data: A Handbook , 1978 .

[23]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[24]  Kenneth H. Pollock,et al.  A capture-recapture model with heterogeneity and behavioural response , 1995, Environmental and Ecological Statistics.

[25]  G. Seber.  A NOTE ON THE MULTIPLE-RECAPTURE CENSUS. , 1965, Biometrika.

[26]  E. George.  Capture—recapture estimation via Gibbs sampling , 1992 .