Confidence Regions for the Contour Lines of Spatial Data

• Activity Number: 314
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Joshua French*
• Companies: University of Colorado Denver
• Keywords: contour lines ; level curves ; geostatistics ; hotspots ; confidence region ; spatial data

Abstract

Contour plots are often used to display the distribution of continuous spatial variables, but the uncertainty associated with the estimated contour lines seldom receives attention. Few methods are available for identifying the true contour line with quantifiable confidence, and typically these methods only deal with the uncertainty at individual locations. Methodology is introduced for constructing a confidence region for the entire contour line of a Gaussian random field at a specified level. The methodology utilizes common geostatistical methods to produce confidence regions containing the entire contour line with high confidence. The validity of this approach is investigated using simulation studies involving several covariance functions, dependence levels, and response quantiles. This methodology is then applied in constructing a confidence region for a contour line of the total monthly precipitation for the state of Colorado in May 1997. Simulation results indicate that this approach works well for the contour lines of Gaussian random fields under a variety of conditions and compares favorably to competing methods.