An examination of belief functions and other monotone capacities

The original motivation for this work was brought about by observations that belief function theory had gained widespread acceptance, especially in the artificial intelligence community, as a convenient representation of uncertainty. Given that belief function theory does not correspond to Bayesian probability theory, it seemed natural to want to examine the new theory, from foundational issues through its potential application to inference and decision problems, to assess the validity of its continued use in real world applications. To obtain sufficient understanding of the belief function calculus, both static representations of uncertainty, corresponding to models that represent the current state of knowledge, and dynamic operations of forming new belief functions from separate static representations are considered. Along the way, realization that belief functions correspond to a subclass of some more general classes of convex sets of probability distributions led to consideration of geometric forms of belief functions and other monotone capacities.;The objectives are, consequently, to understand the limitations of belief function theory and to provide insights into the structure of belief functions and other monotone capacities that might prove useful for theories based on convex sets of probability distributions. Other considerations include the computational complexity of the belief function calculus, information measures for belief functions, and decision theoretic consequences of using belief functions as representations of uncertainty.