The Statistical Analysis of Gaussian and Poisson Signals Near Physical Boundaries

TL;DR

This paper introduces a new frequentist confidence interval construction for Gaussian and Poisson signals near physical boundaries, ensuring coverage and simplicity while unifying two-sided and upper limit intervals.

Contribution

It presents a rigorous, computationally simple method that incorporates physical constraints into estimators, improving interval accuracy near boundaries.

Findings

Effective near unphysical regions

Unifies two-sided and upper limit intervals

Maintains coverage and simplicity

Abstract

We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the pathologies that affect the Likelihood Ratio and related constructions. Away from non-physical regions, the results are exactly the usual central two-sided intervals. The construction is based on including the physical constraint in the derivation of the estimator, leading to an estimator with values that are confined to the physical domain.