Abstract
Presence-only data refer to applicative situations in which a binary response Y can be observed only with respect to certain values of presence (Y=1). In many situations in ecology this problem is evident. For example, when we want to study the prevalence of an animal species from the locations where it was observed. Other applications can be considered also in tax investigations, for example the control of the tax evasion or the control of the illegal labor market from the investigative data by the Tax Authority. In all these situations, the problem can be addressed if there is available information related to the binary response in the form of explanatory covariates. In this talk we present a Bayesian approach to the problem of presence-only data based on a two levels modeling. In particular, we propose a model which from the only observable data, the presences at some locations, and through a modified case-control sampling design, allows us to estimate the effects of the explicative variables jointly with the unknown proportion of presences (the prevalence parameter of the binary response). In this framework, the computation plays a central role and it has been implemented through a MCMC algorithm with a data augmentation step. Applicative results are presented through a comparative Monte Carlo simulation study in which our model is compared with two “strong” benchmarks. The communication is in collaboration with G. Jona Lasinio and N. Golini (University of Rome "La Sapienza") and Antti Penttinen (University of Jyväskylä).