Nonstationary Spatial Process Modeling Through Discrete Mixing

• Activity Number: 445
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jun Duan*+ and Alan E. Gelfand
• Companies: Duke University and Duke University
• Keywords: nonstationary spatial model ; Bayesian spatial model ; finite mixture model ; Gaussian random field ; Gibbs sampling

Abstract

It has been widely recognized that a stationary spatial process model for collected spatial data will usually be inappropriate. We propose a discrete mixture of distributions of Gaussian random field to model a nonstationary spatial process. We begin with a spatial process of a discrete support, which is generally nonstationary. The undesirable ''sparseness'' of its realizations can be overcome by mixing its distribution with that of a white noise, resulting in a finite or countable mixture of distributions of Gaussian random fields. The sample surfaces of the initial spatial process are themselves realizations of a stationary Gaussian random field. Thus a modeling hierarchy of spatial processes is formulated. Fitting and inference for such models, particularly spatial prediction is carried out within a Bayesian framework using Gibbs sampling. The advantages of this model are demonstrated through both simulation study and the analysis of a real data involving precipitation measurements in France.