Dottorato in SCUOLA DI SCIENZE STATISTICHE

Titolo della tesi: Bayesian finite mixture models to account for latent heterogeneity in Capture-Recapture analysis

Gaining knowledge about the size of an animal population in a given area is of particular interest for wildlife management and conservation. Indeed, over the last decades, thousands of species worldwide have been experiencing either an outsize expansion or, more often, a dramatic shrinkage in their abundances: in the worst cases, the latter trend has even led to their extinction. Since carrying out a complete count of animal populations is generally a challenging task, Capture-Recapture models have arisen as valuable tool to estimate the population abundance in the chosen study area, along with some other demographically meaningful parameters. A further ecological key issue for wildlife managers involves the identification of distinct groups of individuals that share similar biological patterns. In this spirit, we bring to light how finite mixtures can be easily embed into Capture-Recapture models in order to carry out jointly the estimation and the classification task. We adopt a Bayesian modelling perspective and this requires ad-hoc solutions in this specific context. Indeed, the literature about Bayesian finite mixture Capture-Recapture models is scarce in addressing some issues that arise in the implementation of the model, such as the common label-switching problem that affect finite mixtures and the specification of suitable prior distributions on component-specific parameters. Notably, we deal with these two issues by proposing two novel flexible classes of joint priors for parameters bounded in the [0,1] set. The idea is to specify joint priors that both retain the flexibility to induce the desired marginal behaviour on the component-specific parameters and help the correct identification of their posterior distributions. The proposals are enhanced by the derivation of some theoretical results. Moreover, we propose a class of parsimonious cross-classified mixture models which can be successfully used to identify different residency patterns in wildlife populations. Notably, when the existence of such patterns is known in advance, finite mixtures can be leveraged to model the structure of the population under study. For each proposed methodology, a simulation study is carried out to investigate its inferential benefits and pitfalls. The application of the outlined models and methods is illustrated on wildlife datasets, revealing their merits and validity in real-world examples and giving insights that may be useful to practitioners.