Bayesian Modeling and MCMC Computation in Linear Logistic Regression for Presence-only Data

Presence-only data are referred to situations in which, given a censoring mechanism, a binary response can be observed only with respect to on outcome, usually called \textit{presence}. In this work we present a Bayesian approach to the problem of presence-only data based on a two levels scheme. A probability law and a case-control design are combined to handle the double source of uncertainty: one due to the censoring and one due to the sampling. We propose a new formalization for the logistic model with presence-only data that allows further insight into inferential issues related to the model. We concentrate on the case of the linear logistic regression and, in order to make inference on…

Spatial Bayesian Modeling of Presence-only Data

Data Augmentation Approach in Bayesian Modelling of Presence-only Data

Abstract Ecologists are interested in prediction of potential distribution of species in suitable areas, essential for planning conservation and management strategies. Unfortunately, often the only available information in such studies is the true presence of the species at few locations of the study area and the associated environmental covariates over the entire area, referred as presence-only data. We propose a Bayesian approach to estimate logistic linear regressions adapted to presence-only data through the introduction of a random approximation of the correction factor in the adjusted logistic model that allows us to overcome the need to know a priori the prevalence of the species.