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On Identifiability in Capture–Recapture Models
Author(s) -
Holzmann Hajo,
Munk Axel,
Zucchini Walter
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2006.00637_1.x
Subject(s) - identifiability , context (archaeology) , econometrics , mixing (physics) , binomial (polynomial) , mark and recapture , mathematics , negative binomial distribution , statistics , computer science , population , geography , poisson distribution , physics , demography , sociology , archaeology , quantum mechanics
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, Biometrics 59, 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.