Objective priors for N-mixture models and model selection of N-mixture models

This is joint work with E. Matechou, X.Wang and C.Villa

Estimating the abundance of a population is a fundamental objective for many wildlife population monitoring programmes and ecological studies. N-mixture models are very commonly used to estimate the absolute abundance of a species based on survey sampling. They provide a simple and cost-effective way to estimate absolute abundance while accounting for imperfect detection. However, a number of issues with N-mixture models have been found when the models are fitted within a classical framework. In particular, parameter identifiability issues and cases where infinite estimates of abundance can arise have been found, while concerns about the considerably different estimates of absolute abundance under different model specifications have also been raised.

In this work, we consider fitting N-mixture models within a Bayesian framework.  We apply a class of objective priors from scoring rules for a number of existing and new formulations of N-mixture models. These objective prior distributions can be proper and are not model dependent. We’ve compared the results of our objective priors to those obtained using standard priors, considering both simulated and real data. Finally, we are working on  model selection of N-mixture models via  Bayes factors as well as other Bayesian tools.