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

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.

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

References in corpus (4)

• Limits and Confidence Intervals in the Presence of Nuisance Parameters
• Estimating limits from Poisson counting data using Dempster--Shafer analysis
• Frequentist Hypothesis Testing with Background Uncertainty
• Likelihood ratio intervals with Bayesian treatment of uncertainties: coverage, power and combined experiments

Cited by in corpus (4)

• Dempster--Shafer Theory and Statistical Inference with Weak Beliefs
• Estimating limits from Poisson counting data using Dempster--Shafer analysis
• Discussion of "On the Birnbaum Argument for the Strong Likelihood Principle"
• AutoGFI: Streamlined Generalized Fiducial Inference for Modern Inference Problems in Models with Additive Errors