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This paper is devoted to expressiveness of hypergraphs for which uncertaintypropagation by local computations via Shenoy/Shafer method applies. It isdemonstrated that for this propagation method for a given joint beliefdistribution no valuation of hyperedges of a hypergraph may provide withsimpler hypergraph structure than valuation of hyperedges by conditionaldistributions. This has vital implication that methods recovering beliefnetworks from data have no better alternative for finding the simplesthypergraph structure for belief propagation. A method for recoverytree-structured belief networks has been developed and specialized forDempster-Shafer belief functions

Beliefs in Markov Trees - From Local Computations to Local Valuation