A Unified Approach to the Classical Statistical Analysis of Small Signals

@article{Feldman1998AUA,
  title={A Unified Approach to the Classical Statistical Analysis of Small Signals},
  author={Gary J. Feldman and Robert D. Cousins},
  journal={Physical Review D},
  year={1998},
  volume={57},
  pages={3873-3889}
}
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… 
Small signal with background: objective confidence intervals and regions for physical parameters from the principle of maximum likelihood
SummaryIt is argued that the choice between one-sided and two-sided confidence intervals must be made according to a rule prior to and independent of the data and it is shown that such a rule was
CL$_s$ Method at Gaussian Limit to Present Searches
TLDR
A new method based on the CLs approach to present results in searches of new physics under the condition that the relevant nuisance parameter space is continuous, using a Gaussian approximation for the distribution of a log-likelihood ratio test statistic in a two-hypotheses testing problem.
Frequentist coverage properties of uncertainty intervals for weak Poisson signals in the presence of background
We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a
Frequentist limit setting in effective field theories
The original frequentist approach for computing confidence intervals involves the construction of the confidence belt which provides a mapping of the observation in data into a subset of values for
Setting confidence intervals for bounded parameters
Setting confidence bounds is an essential part of the reporting of experimental results. Current physics experiments are often done to measure nonnegative parameters that are small and may be zero
Computation of confidence levels for search experiments with fractional event counting and the treatment of systematic errors
A method is described which computes, from an observed sample of events, upper limits for the production rate of new particles, or, for the case of an observed excess of events over background, the
...
...

References

SHOWING 1-10 OF 21 REFERENCES
The Theory of Statistical Inference.
Statistical inference is about figuring out what data are telling us about the world. We gather data related to some question of interest and construct a model of how the data could have been
Statistical Methods in Experimental Physics
Basic Concepts in Probability Convergence and the Law of Large Numbers Probability Distributions Information Decision Theory Theory of Estimators Point Estimation in Practice Interval Estimation Test
Kendall's advanced theory of statistics
Classical Inference and Relationship 5th Ed
  • 1991
28,11.30 2.38,10.30 1.65, 9
    For a related discussion, see Philip W. Anderson
    • Physics Today
    The Theory of Statistical Inference (Wiley
    • New York,
    • 1971
    Statist
    • Assoc. 32 349-56
    • 1937
    Phys
    • Rev. D 24, 110
    • 1981
    Reprinted in A Selection of Early Statistical Papers on
    • Phil. Trans. Royal Soc. London, Series A
    • 1937
    ...
    ...