The Annals of Applied Statistics

Estimating limits from Poisson counting data using Dempster–Shafer analysis

Paul T. Edlefsen, Chuanhai Liu, and Arthur P. Dempster

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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.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 2 (2009), 764-790.

Dates
First available in Project Euclid: 22 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1245676194

Digital Object Identifier
doi:10.1214/00-AOAS223

Mathematical Reviews number (MathSciNet)
MR2750681

Zentralblatt MATH identifier
1166.62004

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

Citation

Edlefsen, Paul T.; Liu, Chuanhai; Dempster, Arthur P. Estimating limits from Poisson counting data using Dempster–Shafer analysis. Ann. Appl. Stat. 3 (2009), no. 2, 764--790. doi:10.1214/00-AOAS223. https://projecteuclid.org/euclid.aoas/1245676194


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