Title: Beliefs in Markov Trees - From Local Computations to Local Valuation,
Abstract: This paper is devoted to expressiveness of hypergraphs for which uncertainty
propagation by local computations via Shenoy/Shafer method applies. It is
demonstrated that for this propagation method for a given joint belief
distribution no valuation of hyperedges of a hypergraph may provide with
simpler hypergraph structure than valuation of hyperedges by conditional
distributions. This has vital implication that methods recovering belief
networks from data have no better alternative for finding the simplest
hypergraph structure for belief propagation. A method for recovery
tree-structured belief networks has been developed and specialized for
Dempster-Shafer belief functions