{
  "id": "1910.11953",
  "version": "v1",
  "published": "2019-10-25T22:04:07.000Z",
  "updated": "2019-10-25T22:04:07.000Z",
  "title": "A Gibbs sampler for a class of random convex polytopes",
  "authors": [
    "Pierre E. Jacob",
    "Ruobin Gong",
    "Paul T. Edlefsen",
    "Arthur P. Dempster"
  ],
  "comment": "24 pages including the appendices",
  "categories": [
    "stat.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-25T22:04:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random convex polytopes",
      "gibbs sampler",
      "computational cost increases",
      "observations",
      "ds framework"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}