The Combination of Confirmatory and Contradictory Statistical Evidence at Low Resolution

• Activity Number: 83 - Your Invited Poster Evening Entertainment: No Longer Board
• Type: Invited
• Date/Time: Sunday, July 30, 2017 : 8:30 PM to 10:30 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Ruobin Gong* and Xiao-Li Meng
• Companies: Harvard University and Harvard University
• Keywords: belief function ; random sets ; Dempster-Shafer ; low-resolution inference ; Bayesian inference ; information aggregation

Abstract

The Dempster-Shafer (DS) theory of belief functions is a generalization of Bayesian inference. It mobilizes the mathematical construct of random sets to describe uncertainty. Random sets make up a language far richer than random variables or vectors. They can truthfully encode partial, low-resolution, or even the lack of knowledge, which are otherwise inexpressible ideas in statistical models. We examine random sets in most plain probabilistic terms, and discuss implications on the aggregation of statistical evidence, in particular confirmatory vs contradictory inputs in this context.