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Estimating limits from Poisson counting data using Dempster-Shafer analysis. (English) Zbl 1166.62004
Summary: 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. The 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.

MSC:
62A01 Foundations and philosophical topics in statistics
62P35 Applications of statistics to physics
65C60 Computational problems in statistics (MSC2010)
Software:
genlimit
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