Bayesian Nonparametric Intensity Estimation for Inhomogeneous Spatial Point Processes

• Activity Number: 291
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yu Ryan Yue*+ and Ji Meng Loh
• Companies: Baruch College, CUNY and AT&T Labs - Research
• Keywords: Adaptive spatial smoothing ; Gaussian Markov random fields ; Gibbs sampling ; Intensity estimation ; Spatial point process

Abstract

In this work we propose a fully Bayesian nonparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points into a regular grid, and then use an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient MCMC simulation algorithm. Compared to existing methods for intensity estimation, e.g., parametric modeling and kernel smoother, the proposed estimator not only avoids the restrictive assumptions on the specific form of the relationship between the intensity function and possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level.