Process Approximation for Analysis of Large Spatial Datasets

• Activity Number: 272
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Gangqiang Xia*+ and Alan E. Gelfand
• Companies: Duke University and Duke University
• Keywords: spatial process ; kernel mixing ; subsampling ; MCMC

Abstract

We consider a customary spatial model with mean structure, Gaussian spatial process, and nugget. When the number of observations N grows large, likelihood-based inference will become unstable and, eventually, infeasible since it involves computing various forms of a large covariance matrix. If we are to fit a Bayesian model and implement some MCMC algorithm, the large covariance matrix will make repeated calculations very slow. We refer to this computational problem as the "Large N problem." We will review a number of ways to deal with the "Large N problem." We propose a discrete kernel mixing approximation model. We adopt a Bayesian framework. We examine the accuracy of our approximation model and compare it with the subsampling model. Examples will be given to illustrate the methods. We will also discuss different representations of the spatial random field and the spatial design for the subsampling strategy.