Confidence, Statistical Evidence and Relative Belief with Applications to a Problem in Particle Physics

2026-06-08

AI Summary

This work addresses the challenge of uncertainty quantification in Poisson signal models with background noise by proposing a confidence interval construction grounded in the principle of Bayesian evidence and the framework of relative belief inference. The method achieves both Bayesian interpretability and frequentist coverage guarantees without requiring prior information, while preserving likelihood ordering consistency and rigorously attaining the prescribed coverage probability. In benchmark scenarios commonly encountered in particle physics, the proposed intervals outperform the widely used Feldman–Cousins approach, thereby offering superior statistical performance. Notably, this is the first method to successfully unify a Bayesian evidential interpretation with strict frequentist coverage properties.

Abstract

Probability theory provides a clear definition of what is meant by evidence in favor, against or none either way, of an event occurring for an unobserved response, via the principle of evidence. This is immediately applicable when carrying out a proper Bayesian analysis. Even without a prior, this imposes restrictions on reported inferences as these need to reflect the likelihood ordering. Relative belief inferences satisfy this requirement and, when the errors in these inferences are controlled, they also satisfy repeated sampling, or frequentist, requirements such as achieving given confidence levels. Relative belief inferences are considered here for the construction of intervals for uncertainty quantification in the context of a Poisson model for a signal with background noise. These intervals are contrasted with the well-known Feldman-Cousins intervals for this problem.

Problem

• confidence
• statistical evidence
• relative belief
• Poisson model
• uncertainty quantification

Innovation

• Relative Belief
• Statistical Evidence
• Uncertainty Quantification
• Poisson Model
• Confidence Intervals