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A Gibbs sampler for a class of random convex polytopes.

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 non-negativity 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.

SUBMITTER: Jacob PE

PROVIDER: S-EPMC8945543 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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A Gibbs sampler for a class of random convex polytopes.

Jacob Pierre E PE Gong Ruobin R Edlefsen Paul T PT Dempster Arthur P AP

Journal of the American Statistical Association 20210422 535

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 ...[more]

PMID: 35340357

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