Quantifying the Uncertainty of Contour Maps

• Activity Number: 89
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 8:30 PM to 9:15 PM
• Sponsor: Korean International Statistical Society
• Author(s): David Bolin*
• Companies: Chalmers University of Technology/University of Gothenburg
• Keywords: Contour maps ; Contour curves ; Excursion sets ; Kriging ; Geostatistics ; Spatial statistics

Abstract

Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use these maps, the uncertainty associated with them has been given a surprisingly small amount of attention. We derive measures of the statistical uncertainty of contour maps that relates to the uncertainty in the estimated field. These measures can be used to decide an appropriate number levels such that the contour map reflects the uncertainty in the spatial field. Computational methods that can be used for practical use in geostatistics and medical imaging are constructed. These methods can be applied to Gaussian Markov random fields and in particular be used in combination with integrated nested Laplace approximations for latent Gaussian models. The methods are demonstrated on an application to temperature estimation.