A Gibbs sampler for a class of random convex polytopes

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

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arXiv · 1910.11953

A Gibbs sampler for a class of random convex polytopes

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

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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 2x2 contingency tables and parameter estimation of the linkage model.

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BibTeX RIS

Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen, Arthur P. Dempster. 2021-01-21. A Gibbs sampler for a class of random convex polytopes. https://arxiv.org/abs/1910.11953

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