  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.
