A Unified Approach to the Classical Statistical Analysis of Small Signals

  title={A Unified Approach to the Classical Statistical Analysis of Small Signals},
  author={Gary J. Feldman and Robert D. Cousins},
  journal={Physical Review D},
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… 
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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
    • Assoc. 32 349-56
    • 1937
    • Rev. D 24, 110
    • 1981
    Reprinted in A Selection of Early Statistical Papers on
    • Phil. Trans. Royal Soc. London, Series A
    • 1937