Quantifying the uncertainty of contour maps

TL;DR

This paper develops statistical measures to quantify the uncertainty of contour maps, providing practical computational methods for Gaussian Markov random fields, with applications in geostatistics and medical imaging.

Contribution

It introduces new measures of uncertainty for contour maps and computational methods for Gaussian Markov random fields, enhancing their interpretability and reliability.

Findings

Methods effectively quantify contour map uncertainty.

Applicable to Gaussian Markov random fields and latent Gaussian models.

Demonstrated on simulated data and temperature estimation.

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 of these maps, the uncertainty associated with them has been given a surprisingly small amount of attention. We derive measures of the statistical uncertainty, or quality, of contour maps, and use these to decide an appropriate number of contour lines, that relates to the uncertainty in the estimated spatial field. For practical use in geostatistics and medical imaging, computational methods are constructed, that 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 simulated data and an application to temperature estimation is presented.