A Gibbs sampler for a class of random convex polytopes

Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen, Arthur P. Dempster

Published 2019-10-25Version 1

We present a Gibbs sampler to implement the Dempster-Shafer (DS) theory of statistical inference for Categorical distributions with arbitrary numbers of categories and observations. The DS framework is trademarked by its three-valued uncertainty assessment (p,q,r), probabilities "for"', "against", and "don't know", associated with formal assertions of interest. The proposed algorithm targets the invariant distribution of a class of random convex polytopes which encapsulate the inference, via establishing an equivalence between the iterative constraints of the vertex configuration and the non-negativity of cycles in a fully connected directed graph. The computational cost increases with the size of the input, linearly with the number of observations and polynomially in the number of non-empty categories. Illustrations of numerical examples include the testing of independence in 2 by 2 contingency tables and parameter estimation of the linkage model. Results are compared to alternative methods of Categorical inference.