A Gibbs Sampler for a Class of Random Convex Polytopes

• Activity Number: 116 - JASA, Theory and Methods Invited Session
• Type: Invited
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: JASA Theory and Methods
• Author(s): Pierre Etienne Jacob* and Ruobin Gong and Paul E Edlefsen and Arthur Dempster
• Companies: Harvard University and Rutgers University and Fred Hutchinson Cancer Research Center and Harvard University
• Keywords: Algorithms; Categorical data analysis; Simulation; Bayesian methods

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 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 for the analysis of count data. 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. The presentation will describe the main ideas underlying the sampler, how to manipulate its output, how to handle categories with zero counts, and how to choose the number of iterations to perform. Illustrations include the testing of independence in 2x2 contingency tables.