Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse

• Activity Number: 73 - Modeling Spatial and Statio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Jieying Jiao* and Guanyu Hu and Jun Yan
• Companies: University of Connecticut and University of Connecticut and University of Connecticut
• Keywords: MCMC; Powered Chinese Restaurant Process; Variable Selection

Abstract

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 approached with a powered Chinese restaurant process prior which prevents unnecessarily small clusters. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo 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.