New UAI 2017 paper - The total belief theorem
The paper 'The total belief theorem', authored by Chunlai Zhou and Fabio Cuzzolin, was accepted for publication at UAI17.
In this paper, motivated by the treatment of conditional constraints in the data association problem, we state and prove the generalisation of the law of total probability to belief functions, as finite random sets.
Our results apply to the case in which Dempster's conditioning is employed. We show that the solution to the resulting total belief problem is in general not unique, whereas it is unique when the a-priori belief function is Bayesian. Examples and case studies underpin the theoretical contributions.
Finally, our results are compared to previous related work on the generalisation of Jeffrey’s rule by Spies and Smets.