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# Final Results of the OPERA Experiment on $${\nu }_{\tau }$$ Appearance in the CNGS Neutrino Beam

Physical Review Letters

American Physical Society (APS)

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### Most cited references22

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### Review of Particle Physics

(2016)
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### A Unified Approach to the Classical Statistical Analysis of Small Signals

(1997)
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 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.
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### Asymptotic formulae for likelihood-based tests of new physics

(2013)
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow one to account for systematic uncertainties. Explicit formulae for the asymptotic distributions of test statistics are derived using results of Wilks and Wald. We motivate and justify the use of a representative data set, called the "Asimov data set", which provides a simple method to obtain the median experimental sensitivity of a search or measurement as well as fluctuations about this expectation.
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### Author and article information

###### Journal
PRLTAO
Physical Review Letters
Phys. Rev. Lett.
American Physical Society (APS)
0031-9007
1079-7114
May 2018
May 22 2018
: 120
: 21
###### Article
10.1103/PhysRevLett.120.211801