  We present a Gibbs sampler for the Dempster-Shafer (DS) approach to
statistical inference for Categorical distributions. The DS framework extends
the Bayesian approach, allows in particular the use of partial prior
information, and yields three-valued uncertainty assessments representing
probabilities "for", "against", and "don't know" about formal assertions of
interest. The proposed algorithm targets the distribution of a class of random
convex polytopes which encapsulate the DS inference. The sampler relies on an
equivalence between the iterative constraints of the vertex configuration and
the non-negativity of cycles in a fully connected directed graph. Illustrations
include the testing of independence in 2x2 contingency tables and parameter
estimation of the linkage model.
