Predicting Gaussian Fields with Unknown Covariance Structure

• 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): Elizabeth C. Shamseldin*+ and Richard L. Smith
• Companies: University of North Carolina, Chapel Hill and University of North Carolina
• Keywords: spatial model ; Bayesian analysis ; kriging ; MCMC ; spatial covariance structure ; covariance estimate error

Abstract

Spatial models are concerned with the underlying covariance structure between a collection of measurements. The theory can be applied to a number of areas including environmental applications such as monitor readings of an atmospheric pollutant such as particulate matter. Traditional spatial systems are modelled as Gaussian random fields whose covariances are some function of the distance between two monitor sites (for example, the exponential or Matern models). "Kriging" is a method of spatial interpolation that uses the covariances to construct optimal estimators of the random field at unobserved locations. However, traditional interval estimates using kriging assume the spatial covariance structure is known, ignoring the possible error in estimating the parameters of a spatial model. Bayesian methods provide one possible resolution of this difficulty, but in general it is unknown whether a Bayesian prediction interval has the correct frequentist coverage probability. We consider traditional kriging methods, Bayesian MCMC methods, and analytic approximations to Bayesian methods to calculate prediction intervals for spatial interpolation.