A Gibbs sampler for a class of random convex polytopes

TL;DR

This paper introduces a Gibbs sampling algorithm for the Dempster-Shafer framework, enabling efficient inference on random convex polytopes that represent uncertainty in categorical data analysis.

Contribution

It develops a novel Gibbs sampler for Dempster-Shafer inference, leveraging graph cycle conditions to sample from complex convex polytopes.

Findings

Effective sampling for DS inference demonstrated on contingency tables

Provides three-valued uncertainty assessments

Applicable to parameter estimation in linkage models

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.