Mark-recapture methods are crucial for studying animals in the wild and for monitoring species threatened by changes in the environment. The assumption that individuals are identified without error is standard in most models of mark-recapture data. However, mistakes can always occur, and it it difficult to account for such errors. The recorded data present a corrupted version of what was actually observed, and naively modelling this data will produce incorrectestimates. However, the possible configurations of true data consistent with the recorded data may be so numerous and complex that it is usually impossible to evaluate the likelihood function.

In this talk, I discuss several contributions I have made to modelling markrecapture data with identification errors. First, I introduce methods that I have developed to model data from populations in which each individual can be identified from multiple marks cannot be linked (e.g., left and right skin pigmentation patterns). Building on the framework of the latent maultinomial model intorduced by Link et al. (Biometrics, 2010), these methods provide Bayesian inference using Markov chain Monte Carlo (MCMC) to sample from the joint posterior distribution of the model parameters and the true data. I Illustrate these methods with data from a photo-identification study of whale sharkes and use this example to show how the MCMC algorithm of Link et al. (2010) can be simplified to produce faster computation.

I also discuss problems with extending these methods to account for more complex identification errors. I show that the MCMC algorithm proposed by Link et al. (2010) may not produce irreducible Markov chains for some models and explain how this problem may be solved with new MCMC algorithms using Markov bases and further tools from algebraic statistics.