A Unified Approach to the Classical Statistical Analysis of Small Signals
Cousins, Robert D.Note: Order does not necessarily reflect citation order of authors.
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CitationFeldman, Gary J., Robert D. Cousing. 1998. A unified approach to the classical statistical analysis of small signals. Physical Review D 57: 3873-3889.
AbstractWe 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 battle-ground 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.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2309662
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