Interpreting Belief Functions as Dirichlet Distributions

Traditional Dempster Shafer belief theory does not provide a simple method for judging the effect of statistical and probabilistic data on belief functions and vice versa. This puts belief theory in isolation from probability theory and hinders fertile cross-disciplinary developments, both from a theoretic and an application point of view. It can be shown that a bijective mapping exists between Dirichlet distributions and Dempster-Shafer belief functions, and the purpose of this paper is to describe this correspondence. This has three main advantages; belief based reasoning can be applied to statistical data, statistical and probabilistic analysis can be applied to belief functions, and it provides a basis for interpreting and visualizing beliefs for the purpose of enhancing human cognition and the usability of belief based reasoning systems.