A Gibbs sampler for a class of random convex polytopes

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  1. Ryan MartinJanuary 29th, 2020 at 08:11 pm

    Thanks for your contribution!  I myself have been thinking about a DS-like approach to the multinomial inference problem and your paper is relevant to this.  I'm definitely interested in this and, after I have a chance to work through some details, I'll post here a formal review.

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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.

Versions

➤  Version 1 (2019-10-25)

Citation

Pierre Jacob, Ruobin Gong, Paul Edlefsen and Arthur Dempster (2019). A Gibbs sampler for a class of random convex polytopes. Researchers.One, https://researchers.one/articles/a-gibbs-sampler-for-a-class-of-random-convex-polytopes/5f52699c36a3e45f17ae7dfc/v1.

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