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Activity Number: 258
Type: Contributed
Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320022 View Presentation
Title: Belief Functions: A Paradigm for Lower-Resolution Probabilistic Inference
Author(s): Ruobin Gong* and Xiao-Li Meng
Companies: Harvard and Harvard
Keywords: belief function ; Dempster-Shafer theory ; coarse data ; objective inference ; Fiducial inference ; multi-resolution inference

Since its introduction in the 1960s, the Dempster-Shafer (DS) theory of belief function has inspired many researchers in domains such as signal processing and artificial intelligence, yet significantly fewer in statistics. The polarized interest can be due to the theory's apparent reliance on rules beyond ordinary probability calculus, which is viewed by many as the fundamental grammar of inference under uncertainty. In making a metaphoric connection to the literature of coarse data modeling (e.g. Heitjan and Rubin '91), we advocate that the DS theory of belief functions is a general framework that allows modeling on the parameter space at a resolution lower than that of intended inference, including at zero, i.e., the state of complete ignorance. This feature of DS theory can be clearly illustrated via a recast of belief function definitions on a probabilistic joint space, which will in turn allow generalizations of combination rules beyond the assumption of independent evidence. We hope to raise the awareness of the versatility of belief functions and its potential contributions to modes of inference, especially in the ubiquitous settings calling for partial apriori knowledge.

Authors who are presenting talks have a * after their name.

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