Abstract #301639

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JSM 2003 Abstract #301639
Activity Number: 168
Type: Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics & the Environment
Abstract - #301639
Title: Using non-Euclidean Distances in Spatial Statistics
Author(s): Konstantin Krivoruchko*+
Companies: ESRI
Address: 380 New York St., Redlands, CA, 92373-8118,
Keywords: spatial statistics ; cost weighted surface ; spatial correlation ; geostatistics ; marked point pattern analysis
Abstract:

Statistical correlation between spatial variables depends on the distance between them and the direction of travel from one to the other. Since most surfaces in nature are convoluted, anything that travels along them is thereby constrained. As a rule, spatial data analysis uses the hypothesis of data homogeneity. Heterogeneity is usually defined by trend in a region as a function of coordinates. Coordinates are usually Cartesian, and distance between observations is Euclidean. We discuss use of the cost weighted distance, a common raster function in GIS that calculates the cost of travel from one cell of a grid to the next, making it the natural choice of the distance metric for spatial prediction. We illustrate how a cost weighted distance is used for geostatistical interpolation using air quality data in California. The usage of cost surface in lattice, point pattern, and marked point pattern data analysis is also covered. To introduce heterogeneity into marked point patterns, we use the cost surface approach to both marks and locations. The dependence between marks and locations is analyzed after their transformation into the same structure.

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