Bayesian analysis of animal abundance data via MCMC

We examine the Bayesian approach to estimating parameters arising from the modelling of animal capture experiments. We discuss the application of the Bayesian approach to a so-called band-return model and look at how Markov chain Monte Carlo techniques can be very naturally applied to problems of this sort. We discuss the problems associated with the maximum likelihood approach to analysing such models and discuss how these problems are overcome by the corresponding Bayesian analysis. For data on mallard ducks, we compare the performance of the "traditional" Gibbs sampler, using the ratio method for non-standard updates, with the Metropolis-within-Gibbs hybrid. The sheer simplicity of the model we consider, where all parameters are probabilities and thus constrained to lie between 0 and I,makes it a natural example for a comparison of this sort and we illustrate how the increase in efficiency per iteration afforded by the hybrid approach appears to be balanced by a corresponding increase in the number of iterations required.