The statistical analysis of Gaussian and Poisson signals near physical boundaries

We propose a construction of frequentist confidence intervals that is effec tive near unphysical regions and unifies the treatment of two-sided and upp er limit intervals. It is rigorous, has coverage, is computationally simple and avoids the pathologies that affect the likelihood ratio and related co nstructions. Away from nonphysical regions, the results are exactly the usu al central two-sided intervals. The construction is based on including the physical constraint in the derivation of the estimator, leading to an estim ator with values that are confined to the physical domain. (C) 2000 America n Institute of Physics. [S0022-2488(00)03508-8].