Spatial point pattern data are routinely encountered. A flexible regression
model for the underlying intensity is essential to characterizing the spatial
point pattern and understanding the impacts of potential risk factors on such
pattern. We propose a Bayesian semiparametric regression model where the
observed spatial points follow a spatial Poisson process with an intensity
function which adjusts a nonparametric baseline intensity with multiplicative
covariate effects. The baseline intensity is piecewise constant, approached
with a powered Chinese restaurant process prior which prevents an unnecessarily
large number of pieces. The parametric regression part allows for variable
selection through the spike-slab prior on the regression coefficients. An
efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the
proposed methods. The performance of the methods is validated in an extensive
simulation study. In application to the locations of Beilschmiedia pendula
trees in the Barro Colorado Island forest dynamics research plot in central
Panama, the spatial heterogeneity is attributed to a subset of soil
measurements in addition to geographic measurements with a spatially varying
baseline intensity.Comment: 21 pages, 7 figure