Estimating Northern Fur Seal Pup Production: A Case Study of Batch Mark Abundance Estimation

We describe a hierarchical N-mixture model for estimating northern fur seal pup production from batch mark-resight data. Our goal was to improve upon a traditional design-based estimation method used for over 50 years. To this end, we propose a hierarchical N-mixture model to account for differences in animal availability for resighting and observer detection probabilities. A Bayesian approach is used for inference with three separate methods proposed for necessary computations. First a straightforward posterior sample is drawn using MCMC. This was considered the gold standard for this analysis. However, we also consider an approximate model-based on Gaussian approximation of the Poisson and binomial distributions used in the exact hierarchical model. By using the Gaussian approximations, analytic integration can be used to marginalize over latent components. Inference can then be made by maximizing the posterior to find the mode. Following this we investigate both delta-method and parametric bootstrap approaches for calculating abundance and the associated standard errors. Each of the three methods produced nearly identical estimates and standard errors, providing support for using Gaussian approximations in other latent abundance models where the abundance is relatively large.