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.
Funding Statement
The first author was funded by research grants from CAPES, Brazil. The second author was funded by grants from CNPq and FAPERJ from Brazil. The support from all these research supporting agencies is gratefully acknowledged by the authors.
Acknowledgments
The authors thank Dr. Carolina Levis for introducing us to the area of presence-only in ecology, Dr. Fernando Figueiredo for useful references in the area, Professor David Warton for valuable insights and guidance in acquiring data, Dr. Guilherme Mazzochini for his aid in acquiring data and for sharing his ecological expertise, Professor Flávio Gonçalves for his technical comments and Professor Ian Renner for making the Eucalyptus data available. They are grateful for the added value provided by the reviewers. Finally, the authors thank the graduate program in statistics at the Federal University of Rio de Janeiro (UFRJ). This paper is based on the doctoral thesis of the first author developed under the supervision of the second author. The authors thank the hospitality provided by the Department of Statistics, UFMG.
Citation
Guido A. Moreira. Dani Gamerman. "Analysis of presence-only data via exact Bayes, with model and effects identification." Ann. Appl. Stat. 16 (3) 1848 - 1867, September 2022. https://doi.org/10.1214/21-AOAS1569
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