New Development of Bayesian Variable Selection Criteria for Spatial Point Process with Applications

Selecting important spatial-dependent variables under the nonhomogeneous spatial Poisson process model is an important topic of great current interest. In this paper, we use the Deviance Information Criterion (DIC) and Logarithm of the Pseudo Marginal Likelihood (LPML) for Bayesian variable selection under the nonhomogeneous spatial Poisson process model. We further derive the new Monte Carlo estimation formula for LPML in the spatial Poisson process setting. Extensive simulation studies are carried out to evaluate the empirical performance of the proposed criteria. The proposed methodology is further applied to the analysis of two large data sets, the Earthquake Hazards Program of United States Geological Survey (USGS) earthquake data and the Forest of Barro Colorado Island (BCI) data.