A Gibbs Sampler for a Class of Random Convex Polytopes
成果类型：
Article
署名作者：
Jacob, Pierre E.; Gong, Ruobin; Edlefsen, Paul T.; Dempster, Arthur P.
署名单位：
Harvard University; Rutgers University System; Rutgers University New Brunswick; Fred Hutchinson Cancer Center
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2021.1881523
发表日期：
2021
页码：
1181-1192
关键词：
摘要：
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 x 2 contingency tables and parameter estimation of the linkage model.