Analysis of presence-only data via exact Bayes, with model and effects identification

Abstract

This paper provides an exact modeling approach for the analysis of presence-only ecological data. Our proposal is also based on frequently used inhomogeneous Poisson processes but does not rely on model approximations, unlike other approaches. Exactness is achieved via a data augmentation scheme. One of the augmented processes can be interpreted as the unobserved occurrences of the relevant species, and its posterior distribution can be used to make predictions of the species over the region of study beyond the observer bias. The data augmentation also leads to a natural Gibbs sampler to make Bayesian inference through MCMC. The proposal shows better performance than the currently standard method based on Poisson process with intensity function depending log-linearly on the covariates. Additionally, an identification problem that arises in the traditional model does not seem to affect our proposal in the analyses of real ecological data.