A theory of Gaussian belief functions

Abstract A Gaussian belief function can be intuitively described as a Gaussian distribution over a hyperplane, whose parallel subhyperplanes are the focal elements. This paper elaborates on the idea of Dempster and Shafer and formally represents a Gaussian belief function as a wide-sense inner product and a linear functional over a variable space, and as their duals over a hyperplane in a sample space. By adapting Dempster's rule to the continuous case, it derives a rule of combination and proves its equivalence to its geometric description by Dempster. It illustrates by examples how mixed knowledge involving linear equations, multivariate Gaussian distributions, and partial ignorance can be represented and combined as Gaussian belief functions.