Bayesian Variable Selection Methods for Log-Gaussian Cox Processes

Abstract

Point patterns are very common in present days of many researchers. The desire to understand the spatial distribution and investigate connections between point patterns and p covariates, that is possibly associated with the event of interest, arises naturally. Generally, not all of the p covariates are useful. Therefore it would be handy to identify the covariate which is, and just use those. Variable selection is an important step when setting a parsimonious model and still occupies the minds of many statisticians. In this work, we investigated Bayesian variable selection methods in the context of point pattern. This work concentrated on the following methods: Kuo and Mallick, Gibbs Variable Selection, and Stochastics Search Variable Selection for log-Gaussian Cox processes. The methods were evaluated in several scenarios: with a different number of covariates that should be included in the model, absence, and presence of multicollinearity and fixed and random effect model. Our results suggest that the three methods, specially Stochastics Search Variable Selection, can work very well with the absence of multicollinearity. We implemented the methods in BUGS.