Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938)
A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Am. Math. Soc. 54(3), 426–482 (1943)
I. Asimov, Franchise, in Isaac Asimov: The Complete Stories, vol. 1 (Broadway Books, New York, 1990)
V. Bartsch, G. Quast, Expected signal observability at future experiments, CMS Note 2005/004 (2003), (available on CMS information server)
ATLAS Collaboration, Expected performance of the ATLAS experiment, detector, trigger and physics. CERN-OPEN-2008-020, Geneva (2008). e-print: arXiv:0901.0512
ALEPH, DELPHI, and L3 and OPAL Collaborations, Search for the standard model higgs boson at LEP. Phys. Lett. B 565, 61–75 (2003). CERN-EP/2003-011
A. Stuart, J.K. Ord, S. Arnold, Kendall’s Advanced Theory of Statistics, Classical Inference and the Linear Model, vol. 2A, 6th edn. (Oxford University Press, London, 1999), and earlier editions by Kendall and Stuart
R.D. Cousins, G.J. Feldman, Phys. Rev. D 57, 3873 (1998)
H. Chernoff, On the distribution of the likelihood ratio. Ann. Math. Stat. 25, 573–578 (1954)
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972). Sect. 26.4.25
Wikipedia, The Free Encyclopedia, Noncentral chi-square distribution. Wikimedia Foundation, Inc., 6 July 2010
T. Aaltonen et al., Phys. Rev. Lett. 104, 061802 (2010). e-Print: arXiv:1001.4162 [hep-ex]
K. Cranmer, Frequentist hypothesis testing with background uncertainty, in Proceedings of PHYSTAT 2003, SLAC, ed. by L. Lyons et al., Stanford, California, 8–11 September 2003, pp. 261–264
T. Junk, Nucl. Instrum. Methods Phys. Res., Sect. A 434, 435 (1999)
A.L. Read, J. Phys. G 28, 2693 (2002)
R.D. Cousins, J.T. Linnemann, J. Tucker, Nucl. Instrum. Methods Phys. Res., Sect. A 595, 480–501 (2008). e-Print: arXiv:physics/0702156v4 [physics.data-an]
E. Gross, O. Vitells, Trial factors or the look elsewhere effect in high energy physics. arXiv:1005.1891 [physics.data-an] (2010)
L. Moneta, K. Belasco, K. Cranmer et al., The RooStats project, in Proceedings of ACAT, Jaipur, India (2010). arXiv:1009.1003 [physics.data-an]. https://twiki.cern.ch/twiki/bin/view/RooStats/
R. Brun, F. Rademakers, ROOT: An object oriented data analysis framework,. Nucl. Instrum. Methods A 389, 81–86 (1997)
W. Verkerke, D.P. Kirkby, The RooFit toolkit for data modeling, in Proceedings for CHEP03 (2003). physics/0306116
F. James, M. Roos, Minuit: a system for function minimization and analysis of the parameter errors and correlations. Comput. Phys. Commun. 10, 343–367 (1975)
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article is available at http://dx.doi.org/10.1140/epjc/s10052-013-2501-z.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Cowan, G., Cranmer, K., Gross, E. et al. Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71, 1554 (2011). https://doi.org/10.1140/epjc/s10052-011-1554-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-011-1554-0