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February 2010 Dempster–Shafer Theory and Statistical Inference with Weak Beliefs
Ryan Martin, Jianchun Zhang, Chuanhai Liu
Statist. Sci. 25(1): 72-87 (February 2010). DOI: 10.1214/10-STS322


The Dempster–Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer science and engineering applications, but has yet to reach the statistical mainstream, perhaps because the DS belief functions do not satisfy long-run frequency properties. Recently, two of the authors proposed an extension of DS, called the weak belief (WB) approach, that can incorporate desirable frequency properties into the DS framework by systematically enlarging the focal elements. The present paper reviews and extends this WB approach. We present a general description of WB in the context of inferential models, its interplay with the DS calculus, and the maximal belief solution. New applications of the WB method in two high-dimensional hypothesis testing problems are given. Simulations show that the WB procedures, suitably calibrated, perform well compared to popular classical methods. Most importantly, the WB approach combines the probabilistic reasoning of DS with the desirable frequency properties of classical statistics.


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Ryan Martin. Jianchun Zhang. Chuanhai Liu. "Dempster–Shafer Theory and Statistical Inference with Weak Beliefs." Statist. Sci. 25 (1) 72 - 87, February 2010.


Published: February 2010
First available in Project Euclid: 3 August 2010

zbMATH: 1328.62040
MathSciNet: MR2741815
Digital Object Identifier: 10.1214/10-STS322

Keywords: Bayesian , Belief functions , Fiducial argument , frequentist , Hypothesis testing , inferential model , nonparametrics

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.25 • No. 1 • February 2010
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