I read population size estimation with capture-recapture in presence of individual misidentification and low recapture arXived by Rémy Fraysse and coauthors on my flight back from Saigon. The setup is one of a capture-recapture experience where potential misidentification (of a recapture individual labelled as new) may occur due to visual identification errors as, e.g., in whale studies. Trying to handle the issue, Yoshizaki et al. (2011) proposed adding one layer to the temporal Darroch model M[t] via a probability α of creating a “ghost” (by failing to recognise a formerly observed individual). When representing the experiment as a partly observed Markov process (as in Dupuis, 1995), this addition brings another completely latent process for misidentification. Completely in the sense that a misidentification is never observed (while a proper identification is). This means there is an issue with identifiability between failing to capture and misidentification, as a new individual may be captured for the first time or misidentified on that round.
Processing this model (i.e., producing a simulation algorithm of the posterior) can be done formally by a Gibbs completion (as in Dupuis, 1995) but this may prove a non-irreducible scheme (Schofer & Bonner, 2015), a problem solved by considering instead Metropolis-Hastings steps. The current paper is an extension of the above to the multiple states Arnason-Schwarz model with no theoretical convergence issue, besides running a large sized completion. It is mostly a simulation experiment with a comparison on different priors on the misspecification rate, some highly informative, others not, with a frequentist assessment of coverage. Given the identifiability issue mentioned above, this is not particularly helpful since it simply exhibits the fact that with the right priors the parameter values are unbiasedly estimated, while a low recapture plus high misidentification setting makes estimation more difficult.
