5 research outputs found
Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse
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
Bayesian Spatial Homogeneity Pursuit Regression for Count Value Data
Spatial regression models are ubiquitous in many different areas such as
environmental science, geoscience, and public health. Exploring relationships
between response variables and covariates with complex spatial patterns is a
very important work. In this paper, we propose a novel spatially clustered
coefficients regression model for count value data based on nonparametric
Bayesian methods. Our proposed method detects the spatial homogeneity of the
Poisson regression coefficients. A Markov random field constraint mixture of
finite mixtures prior provides a consistent estimator of the number of the
clusters of regression coefficients with the geographically neighborhood
information. The theoretical properties of our proposed method are established.
An efficient Markov chain Monte Carlo algorithm is developed by using
multivariate log gamma distribution as a base distribution. Extensive
simulation studies are carried out to examine empirical performance of the
proposed method. Additionally, we analyze Georgia premature deaths data as an
illustration of the effectiveness of our approach