The Predictive Spatial Dirichlet Process with Application to Downscaling
Veronica J. Berrocal1, Sudipto Banerjee2, Alan E. Gelfand3
1Department of Biostatistics, University of Michigan, Ann Arbor, MI, United States; 2Division of Biostatistics, University of Minnesota, Minneapolis, MN, United States; 3Department of Statistical Science, Duke University, Durham, NC, United States

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.

Keywords: Spatial Dirichlet process; Predictive process; Spatially-varying coefficients; Coregionalization

Biography: Veronica Berrocal has earned a Ph.D. in Statistics at the University of Washington in 2007. She has held postdoctoral positions at the U.S. EPA, at Duke University in the Department of Statistical Science and at SAMSI. She is currently an Assistant Professor in the Department of Biostatistics at the University of Michigan.