Hierarchical Poisson/Gamma Random Field Model

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jian Kang*+ and Timothy D. Johnson and Thomas E. Nichols
• Companies: University of Michigan and University of Michigan and University of Warwick
• Keywords: Spatial Point Processes ; Random Intensity Measure ; Classification Model ; Nonparametric Bayes ; Hierarchical Model

Abstract

To jointly analyze multiple groups of spatial point patterns, we propose a non-parametric Bayesian modeling approach that extends the Poisson/Gamma random field model (Wolpert and Ickstadt, 1998). In particular, each group of point patterns is modeled as a Poisson point process driven by a random intensity that is a kernel convolution of a gamma random field. The group-level gamma random fields are linked and modeled as a realization of a common gamma random field shared by all the groups. We resort to a hybrid algorithm with adaptive reject sampling embedded in a Markov chain Monte Carlo algorithm for posterior inference. Also, our model can be used to build a classifier of group label given spatial point patterns based on the corresponding posterior predictive probability. We illustrate our models on simulated examples and two real applications.