Variable selection for spatial Poisson point processes via a regularization method

It is often of interest to use regression analysis to study the relationship between occurrence of events in space and spatially-indexed covariates. One model for such regression analysis is the Poisson point process. Here, we develop a method to perform the selection of covariates and the estimation of model parameters simultaneously for this model via a regularization method. We assess the finite-sample properties of our method with a simulation study. In addition, we propose a variant of our method that allows the selection of covariates at multiple pixel resolutions. For illustration, we consider the locations of a tree species, Beilschmiedia pendula, in a study plot at Barro Colorado Island in central Panama. We find that Beilschmiedia pendula occurs in greater abundance at locations with higher elevation and steeper slope. Also, we identify three species to which Beilschmiedia pendula tends to be attracted, two species by which it appears to be repelled, and a species with no apparent relationship.