Analyzing Non-stationary Spatial Data Using Piecewise Gaussian Processes

• Activity Number: 354
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Hyoung-Moon Kim*+ and Bani Mallick
• Affiliation(s): Texas A&M University, Corpus Christi and Texas A&M University
• Keywords: Voronoi tessellation ; kriging ; Bayes factor ; Reversible jump MCMC ; model averaging

Abstract

Spatial processes are an important modeling tool for geostatistical problems. Classical geostatistics is based on the assumption of stationarity and rely on a variogram model to account for the spatial dependence in the observed data. It is widely recognized that in several occasions the assumption of constant spatial structure throughout the sampling region is violated.

In this paper a new class of nonstationary processes is proposed based on piecewise stationary processes. In particular, we have used piecewise Gaussian processes due to its nice interpretation and direct link with piecewise kriging, but the methodology can be extended for any piecewise stationary processes. Voronoi tessellation is used to partition the non-stationary random field into locally stationary isotropic random fields. Bayesian hierarchical model is used to incorporate uncertainty in the specification of the nonstationarity. Reversible jump MCMC (Markov chain Monte Carlo) is exploited to obtain the number and location of the partitions.

This method is applied to permeability data of the La Cira field in the Magdalena middle basin, Colombia, South America.