A Gibbs sampler for a class of random convex polytopes.

Area of Science:

• Statistics
• Computational Statistics
• Data Science

Background:

• The Dempster-Shafer (DS) framework offers an alternative to Bayesian inference, accommodating partial prior information.
• DS theory provides a framework for representing uncertainty with three values: 'for', 'against', and 'don't know'.

Purpose of the Study:

• To introduce a novel Gibbs sampler for statistical inference within the Dempster-Shafer framework for categorical distributions.
• To enable the use of partial prior information and generate three-valued uncertainty assessments.

Main Methods:

• A Gibbs sampler algorithm is proposed, targeting the distribution of random convex polytopes that represent DS inference.
• The sampler leverages an equivalence between iterative constraints of vertex configurations and non-negative cycles in directed graphs.

Main Results:

• The developed Gibbs sampler effectively implements the Dempster-Shafer approach for categorical data.
• Illustrative applications demonstrate successful testing of independence in 2x2 contingency tables and linkage model parameter estimation.

Conclusions:

• The proposed Gibbs sampler provides a computational tool for Dempster-Shafer statistical inference.
• This approach enhances uncertainty quantification by incorporating 'don't know' states, applicable to various statistical problems.