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

TL;DR

This paper introduces a Dempster--Shafer statistical method for estimating limits from Poisson counting data, reducing reliance on priors and demonstrating favorable results compared to existing approaches.

Contribution

It applies Dempster--Shafer analysis to Poisson data, providing a prior-independent framework for limit estimation with practical advantages.

Findings

Favorable comparison with other methods on the Banff challenge

Reduced prior dependence in limit estimation

Demonstrates practical and theoretical benefits of DS approach

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.