Two-Dimensional Bayesian Information Criteria for Spatial Poisson Point Process (Case Study: Spatial Distribution Modeling of a Tree Species in Barro Colorado Island)

Abstract

Species distribution modeling, where the distribution of specific species locations is connected to the environmental factors. Such data is called spatial point patterns, and the modeling is conducted based on the spatial point process. One central question is to select the best subset of such environmental factors that explain the best species distribution. Besides, the computational issue arises when numerous environmental factor is available. This paper focuses on developing a computational strategy to deal with variable selection through regularization methods for Poisson point process. In particular, two-dimensional Bayesian Information Criteria is proposed to select two types of tuning parameters. The first parameter plays the role of decreasing bias, and the second one improves the variances. Finally, the methodology is applied to tropical rain forest data in Barro Corrolado Island. The results show the adaptive elastic net regularization with the tuning parameters produces the best inhomogeneous poisson point process model.