A comparison of Bayes', Dempster–Shafer and Endorsement theories for managing knowledge uncertainty in the context of land cover monitoring

Abstract

Automated approaches for updating the Land Cover of Scotland 1988 are being developed. This paper compares the suitability of three formalisms for combining information about semi-natural land cover features: Bayesian probabilities, Dempster–Shafer theory and Endorsement theory. The formalisms are evaluated using an example change problem. We would like to determine change direction using modelled knowledge of how land cover features are mapped manually. This evidence includes bio-geographic data, expert heuristics or rules of thumb, reflectance data and knowledge specific to land cover classes and land cover transitions. Bayes' and Dempster–Shafer theories are shown to be more useful where evidence is expressed numerically. We show Bayes' theorem to be an approach that does not work in the example change problem because it requires a complete probability model that is not provided by the evidence. Reworking the data to fit the problem changes the question that is asked of the evidence. The Dempster–Shafer approach was also found to be unsuited to this problem as it required a disaggregation of the available evidence. It is most suited to situations where the evidence is incomplete. In contrast, Endorsement theory is able to represent different kinds of evidence because of its symbolic approach, specifying precisely the strength of belief given to evidence and how it was combined. Applying Endorsement theory facilitates easier, greater and more transparent integration of spatial data. This is an advantage during the development of automated systems.