Abstract
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 nonnegativity of cycles in a fully connected directed graph. Illustrations include the testing of independence in 2 × 2 contingency tables and parameter estimation of the linkage model.
Supplementary Materials
The supplementary materials describe the choice of sampling mechanism, its effect on statistical inference and its relation with the Gumbel-max trick. They also describe the convergence rate of the algorithm in a simple case and provide reminders on empirical convergence analysis using coupled Markov chains.
National Institute of Allergy and Infectious Diseases;
Acknowledgments
The authors thank Rahul Mazumder for useful advice on linear programming.