Directional rates of change under spatial process models
成果类型：
Article
署名作者：
Banerjee, S; Gelfand, AE; Sirmans, CF
署名单位：
University of Minnesota System; University of Minnesota Twin Cities; Duke University; University of Connecticut
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/C16214503000000909
发表日期：
2003
页码：
946-954
关键词：
摘要：
Spatial process models are now widely used for inference in many areas of application. In such contexts interest is often in the rate of change of a spatial surface at a given location in a given direction. Examples include temperature or rainfall gradients in meteorology, pollution gradients for environmental data, and surface roughness assessment for digital elevation models. Because 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 as developed by Stein and Banerjee and Gelfand. We obtain complete distribution theory results under the assumptions of a stationary Gaussian process model either for the data or for spatial random effects. We present inference under a Bayesian framework which, in this setting, presents several advantages. Finally, we illustrate our methodology with a simulated dataset and also with a real estate dataset consisting of selling prices of individual homes.