A Gibbs Sampler for a Class of Random Convex Polytopes
针对分类数据的Dempster-Shafer统计推断，提出一种吉布斯采样算法，通过随机凸多面体分布实现部分先验信息下的不确定性评估，适用于独立性检验和参数估计。
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.