JSM 2004 - Toronto

Abstract #300176

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Activity Number: 366
Type: Invited
Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
Sponsor: ENAR
Abstract - #300176
Title: On Bayesian Wombling: Estimating Spatial Gradients
Author(s): Alan E. Gelfand*+ and Sudipto Banerjee
Companies: Duke University and University of Minnesota
Address: Institute of Statistics and Decision Science, Durham, NC, 27708-0251,
Keywords:
Abstract:

Spatial process models are now widely used for inference in many areas of application. In such contexts interest often lies in estimating the rate of change of a spatial surface at a given location in a given direction. This problem, known as "wombling,'' after a foundational paper by William Womble, is encountered in several scientific disciplines. Examples include temperature or rainfall gradients in meteorology, pollution gradients for environmental data, and surface roughness assessment for digital elevation models. Since the spatial surface is viewed as a random realization, all such rates of change are random as well. We formalize the notions of directional finite difference processes and directional derivative processes building upon the concept of mean square differentiability and obtain complete distribution theory results for stationary Gaussian process models. We present inference under a Bayesian framework which, in this setting, presents several modeling advantages. Illustrations are provided with simple and complex spatial models.

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