Belief Functions: Theory and Algorithms

The subject of this thesis is belief function theory and its application in different contexts. Belief function theory can be interpreted as a generalization of Bayesian probability theory and makes it possible to distinguish between different types of uncertainty. In this thesis, applications of belief function theory are explored both on a theoretical and on an algorithmic level. The problem of exponential complexity associated with belief function inference is addressed in this thesis by showing how efficient algorithms can be developed based on Monte-Carlo approximations and exploitation of independence. The effectiveness of these algorithms is demonstrated in applications to particle filtering, simultaneous localization and mapping, and active classification.