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Title: Unified approach to the classical statistical analysis of small signals

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. {copyright} {ital 1998} {ital The American Physical Society}

Authors:
 [1];  [2]
  1. Department of Physics, Harvard University, Cambridge, Massachusetts02138 (United States)
  2. Department of Physics and Astronomy, University of California, Los Angeles, California90095 (United States)
Publication Date:
OSTI Identifier:
624772
Resource Type:
Journal Article
Journal Name:
Physical Review, D
Additional Journal Information:
Journal Volume: 57; Journal Issue: 7; Other Information: PBD: Apr 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; STOCHASTIC PROCESSES; GAUSSIAN PROCESSES; SIGNALS; STATISTICS; NEUTRINO OSCILLATION; MAXIMUM-LIKELIHOOD FIT

Citation Formats

Feldman, G.J., and Cousins, R.D. Unified approach to the classical statistical analysis of small signals. United States: N. p., 1998. Web. doi:10.1103/PhysRevD.57.3873.
Feldman, G.J., & Cousins, R.D. Unified approach to the classical statistical analysis of small signals. United States. doi:10.1103/PhysRevD.57.3873.
Feldman, G.J., and Cousins, R.D. Wed . "Unified approach to the classical statistical analysis of small signals". United States. doi:10.1103/PhysRevD.57.3873.
@article{osti_624772,
title = {Unified approach to the classical statistical analysis of small signals},
author = {Feldman, G.J. and Cousins, R.D.},
abstractNote = {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. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevD.57.3873},
journal = {Physical Review, D},
number = 7,
volume = 57,
place = {United States},
year = {1998},
month = {4}
}