Uncovering a Latent Multinomial: Analysis of Mark-Recapture Data with Misidentification

Natural tags based on DNA fingerprints or natural features of animals are now becoming very widely used in wildlife population biology. However, classic capture-recapture models do not allow for misidentification of animals which is a potentially very serious problem with natural tags. Statistical analysis of misidentification processes is extremely difficult using traditional likelihood methods but is easily handled using Bayesian methods. We present a general framework for Bayesian analysis of categorical data arising from a latent multinomial distribution. Although our work is motivated by a specific model for misidentification in closed population capture-recapture analyses, with crucial assumptions which may not always be appropriate, the methods we develop extend naturally to a variety of other models with similar structure. Suppose that observed frequencies f are a known linear transformation f = A'x of a latent multinomial variable x with cell probability vector pi = pi(theta). Given that full conditional distributions [theta vertical bar x] can be sampled, implementation of Gibbs sampling requires only that we can sample from the full conditional distribution [x vertical bar f, theta], which is made possible by knowledge of the null space of A'. We illustrate the approach using two data sets with individual misidentification, one simulated, the other summarizing recapture data for salamanders based on natural marks.