Bayesian Three-Dimensional Random-Shape Spatial Clustering

• Activity Number: 674
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Timothy D. Johnson*+ and Jian Kang
• Companies: University of Michigan and University of Michigan
• Keywords: Spherical harmonics ; Marked spatial point processes ; Random functions ; Associated Legendre functions

Abstract

We present a Bayesian random-shape spatial cluster model that generalizes the Mat\'ern cluster process in 3D. The Mat\'ern cluster process assumes that points cluster in spheres. In some applications, spatial point patterns may cluster in configurations that are not well represented by a sphere. Overlapping spherical clusters may be able to capture some features of these clusters, however, the number and shape of unique clusters may also be of interest and, thus, presents problems. The key idea is to utilize the spectral representation of a homogeneous and isotropic Gaussian process on the unit sphere. The random radial function of the shapes is obtained by exponentiating and transforming this process to 3D Euclidean space. We apply our model to a meta-analysis of Neuroimaging data. The general idea may also be applied in random shape analyses.