Bayesian Nonparametric Modeling for Spatial Data

• Activity Number: 258
• Type: Invited
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): Athanasios Kottas*+ and Alan E. Gelfand and Steven MacEachern
• Companies: University of California, Santa Cruz and Duke University and Ohio State University
• Keywords: dependent Dirichlet processes ; Dirichlet process mixture models ; Gaussian processes ; nonstationarity ; spatial generalized linear models

Abstract

Customary modeling for continuous point-referenced spatial data assumes a Gaussian process, which is often taken to be stationary. Here, we propose a random spatial process that is neither Gaussian nor stationary. We first develop a dependent Dirichlet process (DP) model for spatial data. Next, we introduce mixing through dependent DPs and examine properties of the resulting models. In the Bayesian framework, posterior inference is implemented using Markov chain Monte Carlo (MCMC) methods. Spatial prediction raises interesting questions but can be handled using the MCMC output. The hierarchical nature of our modeling allows important extensions to nonparametric spatial generalized linear models (GLMs). The dependent DP framework yields interesting correlation structures and provides more flexible distributional specifications than traditional spatial glms, e.g., binomial response and Poisson count models. Applications include modeling and prediction for disease incidence employing the dependent DP model for the spatial variation in the probability of disease.