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June 2009 Estimating limits from Poisson counting data using Dempster–Shafer analysis
Paul T. Edlefsen, Chuanhai Liu, Arthur P. Dempster
Ann. Appl. Stat. 3(2): 764-790 (June 2009). DOI: 10.1214/00-AOAS223

Abstract

We present a Dempster–Shafer (DS) approach to estimating limits from Poisson counting data with nuisance parameters. Dempster–Shafer is a statistical framework that generalizes Bayesian statistics. DS calculus augments traditional probability by allowing mass to be distributed over power sets of the event space. This eliminates the Bayesian dependence on prior distributions while allowing the incorporation of prior information when it is available. We use the Poisson Dempster–Shafer model (DSM) to derive a posterior DSM for the “Banff upper limits challenge” three-Poisson model. The results compare favorably with other approaches, demonstrating the utility of the approach. We argue that the reduced dependence on priors afforded by the Dempster–Shafer framework is both practically and theoretically desirable.

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Paul T. Edlefsen. Chuanhai Liu. Arthur P. Dempster. "Estimating limits from Poisson counting data using Dempster–Shafer analysis." Ann. Appl. Stat. 3 (2) 764 - 790, June 2009. https://doi.org/10.1214/00-AOAS223

Information

Published: June 2009
First available in Project Euclid: 22 June 2009

zbMATH: 1166.62004
MathSciNet: MR2750681
Digital Object Identifier: 10.1214/00-AOAS223

Keywords: Bayesian , belief function , Dempster–Shafer , evidence theory , Higgs boson , high-energy physics , Poisson

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 2 • June 2009
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