A Gibbs Sampler for a Class of Random Convex Polytopes

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 probabiliti...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2021-07, Vol.116 (535), p.1181-1192
Main Authors: Jacob, Pierre E., Gong, Ruobin, Edlefsen, Paul T., Dempster, Arthur P.
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Bayesian methods
Categorical data analysis
Contingency
Contingency tables
Graph theory
Iterative methods
Parameter estimation
Polytopes
Regression analysis
Simulation
Statistical inference
Statistical methods
Statistics
Uncertainty
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Summary: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 nonnegativity 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.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.2021.1881523