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

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