JSM 2005 - Toronto

Abstract #302450

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 432
Type: Invited
Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #302450
Title: Gradients Gone Wild
Author(s): Alan E. Gelfand*+
Companies: Duke University
Address: Institute of Statistics & Decision Sciences, Durham, NC, 27708, USA
Keywords: directional derivatives ; Gaussian processes ; spatial regression ; Bayesian nonparametrics
Abstract:

The topography of spatial surfaces is examined in this paper. In particular, assuming sufficient smoothness, one can investigate gradients to a spatial surface. When the surface is a random realization of a spatial process, under suitable conditions for the process covariance function, we can consider the ensemble of gradients at different locations and in different directions. Banerjee, Gelfand, and Sirmans (2003) developed the necessary distribution theory and inference in the case of a Gaussian process. In this talk, we will go beyond this work, looking at (i) the random surface that arises as a realization of a mean process, which is, itself, a linear transformation of a multivariate spatial process, (ii) the random surface that arises through a nonparametric specification such as the spatial Dirichlet process, (iii) the random surface that evolves in time, discretized so we have a dynamic spatial process model---perhaps with evolving Gaussian processes or spatial Dirichlet processes. Theoretical results (convergence and distribution theory) and applications (exposure and land values) will be presented.

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Revised March 2005