Bayesian Discovery of Species in Multiple Areas

In ecology, the description of species composition and biodiversity calls for statistical methods that involve estimating features of interest in unobserved samples based on an observed one. In the last decade, the Bayesian nonparametrics literature has thoroughly investigated the case where data arise from a homogeneous population. In this work, we propose a novel framework to address heterogeneous populations, specifically dealing with scenarios where data arise from two areas. This setting significantly increases the mathematical complexity of the problem and, as a consequence, it has received limited attention in the literature. While early approaches leverage computational methods, we provide a distributional theory for the in-sample analysis of any observed sample and enable out-of-sample prediction for the number of unseen distinct and shared species in additional samples of arbitrary sizes. The latter also extends the frequentist estimators, which solely deal with one-step-ahead prediction. Furthermore, our results can be applied to address sample size determination in sampling problems aimed at detecting distinct and shared species. Our results are illustrated in a real-world dataset concerning a population of ants in the city of Trieste.