On Identifiability in Capture–Recapture Models

Authors

  • Hajo Holzmann,

    1. Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Maschmühlenweg 8-10, D–37073 Göttingen, Germany
    Search for more papers by this author
  • Axel Munk,

    Corresponding author
    1. Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Maschmühlenweg 8-10, D–37073 Göttingen, Germany
      email:munk@math.uni-goettingen.de
    Search for more papers by this author
  • Walter Zucchini

    1. Institut für Statistik und Ökonometrie, Platz der Göttinger Sieben 5, D–37073 Göttingen, Germany
    Search for more papers by this author

email:munk@math.uni-goettingen.de

Abstract

Summary We study the issue of identifiability of mixture models in the context of capture–recapture abundance estimation for closed populations. Such models are used to take account of individual heterogeneity in capture probabilities, but their validity was recently questioned by Link (2003, Biometrics59, 1123–1130) on the basis of their nonidentifiability. We give a general criterion for identifiability of the mixing distribution, and apply it to establish identifiability within families of mixing distributions that are commonly used in this context, including finite and beta mixtures. Our analysis covers binomial and geometrically distributed outcomes. In an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models.

Ancillary