Estimating limits from Poisson counting data using Dempster--Shafer analysis

Details Estimating limits from Poisson counting data using Dempster--Shafer analysis Estimating limits from Poisson counting data using Dempster--Shafer analysis

2008-12-09

arxiv.org/abs/0812.1690v2

Annals of Applied Statistics 2009, Vol. 3, No. 2, 764-790

Statistics

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Published in at http://dx.doi.org/10.1214/00-AOAS223 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/00-AOAS223

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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