  The latent multinomial model (LMM) model of Link et al. (2010) provided a
general framework for modelling mark-recapture data with potential errors in
identification. Key to this approach was a Markov chain Monte Carlo (MCMC)
scheme for sampling possible configurations of the counts true capture
histories that could have generated the observed data. This MCMC algorithm used
vectors from a basis for the kernel of the linear map between the true and
observed counts to move between the possible configurations of the true data.
Schofield and Bonner (2015) showed that a strict basis was sufficient for some
models of the errors, including the model presented by Link et al. (2010), but
a larger set called a Markov basis may be required for more complex models. We
address two further challenges with this approach: 1) that models with more
complex error mechanisms do not fit easily within the LMM and 2) that the
Markov basis can be difficult or impossible to compute for even moderate sized
studies. We address these issues by extending the LMM to separately model the
capture/demographic process and the error process and by developing a new MCMC
sampling scheme using dynamic Markov bases. Our work is motivated by a study of
Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to
compare the use of PIT tags, with perfect identification, and brands, which are
prone to error, when estimating survival rates.
