Unified approach to the classical statistical analysis of small signals

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ID: 267046
1998
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Abstract
We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battleground between classical and Bayesian statistics: Poisson processes with background and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.
Reference Key
feldman1998physicalunified Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Gary J. Feldman;Robert D. Cousins;
Journal physical review d
Year 1998
DOI
doi:10.1103/PhysRevD.57.3873
URL
https://doi.org/10.1103%2FPhysRevD.57.3873
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