JSM 2004 - Toronto

Abstract #301544

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Activity Number: 272
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301544
Title: Process Approximation for Analysis of Large Spatial Datasets
Author(s): Gangqiang Xia*+ and Alan E. Gelfand
Companies: Duke University and Duke University
Address: PO Box 90251, Durham, NC, 27708,
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.


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