The Predictive Spatial Dirichlet Process with Application to Downscaling

• Activity Number: 335
• Type: Topic Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Veronica J. Berrocal*+ and Sudipto Banerjee and Alan E. Gelfand
• Companies: Statistical and Applied Mathematical Sciences Institute and University of Minnesota and Duke University
• Keywords: spatial Dirichlet Process ; predictive process ; interpolation ; downscaling ; linear model of coregionalization

Abstract

The spatial Dirichlet process is a flexible mixture model process that allows to represent a spatial process without assuming Gaussianity or stationarity. Prediction of spatial DPs at unobserved locations requires specifying the locations of the sites at which prediction is sought prior to fitting the model. Here, we propose a method to circumvent these difficulties by implementing the predictive process approach of Banerjee et al. (2008). In particular, our predictive spatial DP uses the nodes of the predictive process as the sites associated with the atoms of the spatial DP. Then, prediction at any site is handled deterministically, as in the predictive process framework. As an application, we present our method in the context of downscaling, extending the downscaler of Berrocal et al. (2010), modeling the spatially varying coefficients as a correlated bivariate predictive spatial DP.