The Statistical Analysis of Gaussian and Poisson Signals Near Physical Boundaries

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.