메뉴 건너뛰기




Volumn 595, Issue 2, 2008, Pages 480-501

Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process

Author keywords

Confidence interval; Hypothesis test; Systematic uncertainties

Indexed keywords

BOOLEAN FUNCTIONS; ERROR ANALYSIS; GAMMA RAYS; HIGH ENERGY PHYSICS; IONIZING RADIATION; POISSON EQUATION; POISSON RATIO; SATELLITE OBSERVATORIES; STATISTICAL METHODS; THREE TERM CONTROL SYSTEMS;

EID: 51649119067     PISSN: 01689002     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nima.2008.07.086     Document Type: Article
Times cited : (194)

References (50)
  • 1
    • 84894206361 scopus 로고    scopus 로고
    • For a recent review, see R.D. Cousins, Treatment of nuisance parameters in high energy physics, and possible justifications and improvements in the statistics literature, in: Proceedings of PhyStat 05: Statistical Problems in Particle Physics, Astrophysics and Cosmology (Oxford, September 12-15, 2005) 〈http://www.physics.ox.ac.uk/phystat05/proceedings/〉. See also the response following by N. Reid.
    • For a recent review, see R.D. Cousins, Treatment of nuisance parameters in high energy physics, and possible justifications and improvements in the statistics literature, in: Proceedings of PhyStat 05: Statistical Problems in Particle Physics, Astrophysics and Cosmology (Oxford, September 12-15, 2005) 〈http://www.physics.ox.ac.uk/phystat05/proceedings/〉. See also the response following by N. Reid.
  • 2
    • 51649098299 scopus 로고    scopus 로고
    • For a comprehensive discussion of hypothesis testing, see A. Stuart, K. Ord, S. Arnold, Kendall's Advanced Theory of Statistics, vol. 2A, sixth ed., Arnold, London, 1999, and earlier editions by Kendall and Stuart. From the formal correspondence between hypothesis tests and confidence intervals in Chapter 20, all the frequentist hypothesis tests in this paper can be restated in terms of confidence intervals and limits.
    • For a comprehensive discussion of hypothesis testing, see A. Stuart, K. Ord, S. Arnold, Kendall's Advanced Theory of Statistics, vol. 2A, sixth ed., Arnold, London, 1999, and earlier editions by Kendall and Stuart. From the formal correspondence between hypothesis tests and confidence intervals in Chapter 20, all the frequentist hypothesis tests in this paper can be restated in terms of confidence intervals and limits.
  • 5
    • 51649114673 scopus 로고    scopus 로고
    • J.T. Linnemann, Measures of significance in HEP and astrophysics, in: Proceedings of PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology, SLAC, Stanford, CA, USA, September 8-11, 2003 [arXiv:physics/0312059] 〈http://www.slac.stanford.edu/econf/C030908/papers/MOBT001.pdf〉.
    • J.T. Linnemann, Measures of significance in HEP and astrophysics, in: Proceedings of PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology, SLAC, Stanford, CA, USA, September 8-11, 2003 [arXiv:physics/0312059] 〈http://www.slac.stanford.edu/econf/C030908/papers/MOBT001.pdf〉.
  • 6
    • 0039735159 scopus 로고
    • The figures are missing from the published paper but are in the Ph.D. Thesis of Zhang, who kindly provided them to us.
    • Zhang S.N., and Ramsden D. Exp. Astron. 1 (1990) 145 The figures are missing from the published paper but are in the Ph.D. Thesis of Zhang, who kindly provided them to us.
    • (1990) Exp. Astron. , vol.1 , pp. 145
    • Zhang, S.N.1    Ramsden, D.2
  • 7
    • 51649085481 scopus 로고    scopus 로고
    • F. James, MINUIT. Function Minimization and Error Analysis 〈http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/minmain.html〉.
    • F. James, MINUIT. Function Minimization and Error Analysis 〈http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/minmain.html〉.
  • 11
    • 51649124418 scopus 로고    scopus 로고
    • K.S. Cranmer, Frequentist hypothesis testing with background uncertainty, in: Proceedings of PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology, SLAC, Stanford, CA, USA, September 8-11, 2003 [arXiv:physics/0310108] 〈http://www.slac.stanford.edu/econf/C030908/papers/WEMT004.pdf〉.
    • K.S. Cranmer, Frequentist hypothesis testing with background uncertainty, in: Proceedings of PhyStat 2003: Statistical Problems in Particle Physics, Astrophysics, and Cosmology, SLAC, Stanford, CA, USA, September 8-11, 2003 [arXiv:physics/0310108] 〈http://www.slac.stanford.edu/econf/C030908/papers/WEMT004.pdf〉.
  • 12
    • 84894135513 scopus 로고    scopus 로고
    • b (b in his notation) is known by the experimenter when calculating the rms of the Gaussian but unknown when calculating the mean. This does not cause a significant problem for his example of b = 100 in which he used a self-consistent set of numbers. But for the profile likelihood for the more general Gaussian-mean problem, one must use Eqn. 21 in the present paper (which is consistent with the normal equations used by Ref. [10]).
    • b (b in his notation) is known by the experimenter when calculating the rms of the Gaussian but unknown when calculating the mean. This does not cause a significant problem for his example of b = 100 in which he used a self-consistent set of numbers. But for the profile likelihood for the more general Gaussian-mean problem, one must use Eqn. 21 in the present paper (which is consistent with the normal equations used by Ref. [10]).
  • 13
    • 84862830511 scopus 로고    scopus 로고
    • J. Heinrich, Review of the Banff challenge on upper limits, in: Talk at PHYSTAT-LHC Workshop on Statistical Issues for LHC Physics, CERN, 27-29 June 2007 〈http://phystat-lhc.web.cern.ch/phystat-lhc/〉.
    • J. Heinrich, Review of the Banff challenge on upper limits, in: Talk at PHYSTAT-LHC Workshop on Statistical Issues for LHC Physics, CERN, 27-29 June 2007 〈http://phystat-lhc.web.cern.ch/phystat-lhc/〉.
  • 19
    • 51649099658 scopus 로고    scopus 로고
    • W.H. Press, et al., Numerical Recipes in C, second ed., Cambridge, 1992.
    • W.H. Press, et al., Numerical Recipes in C, second ed., Cambridge, 1992.
  • 20
    • 51649088597 scopus 로고    scopus 로고
    • ROOT, An object-oriented data analysis framework 〈http://root.cern.ch〉.
    • ROOT, An object-oriented data analysis framework 〈http://root.cern.ch〉.
  • 21
    • 0007025295 scopus 로고
    • See also 〈http://lib.stat.cmu.edu/apstat/63〉
    • Majumder K.L., and Bhattacharjee G.P. Appl. Stat. 22 (1973) 409. http://lib.stat.cmu.edu/apstat/63 See also 〈http://lib.stat.cmu.edu/apstat/63〉
    • (1973) Appl. Stat. , vol.22 , pp. 409
    • Majumder, K.L.1    Bhattacharjee, G.P.2
  • 27
    • 51649124841 scopus 로고    scopus 로고
    • A. Stuart, J. Keith Ord, Kendall's Advanced Theory of Statistics, Distribution Theory, vol. 1, sixth ed., Arnold, London, 1994 (see also earlier editions by Kendall and Stuart).
    • A. Stuart, J. Keith Ord, Kendall's Advanced Theory of Statistics, Distribution Theory, vol. 1, sixth ed., Arnold, London, 1994 (see also earlier editions by Kendall and Stuart).
  • 28
    • 51649115205 scopus 로고    scopus 로고
    • L. Demortier, private communication, including the pointer to Ref. [24].
    • L. Demortier, private communication, including the pointer to Ref. [24].
  • 29
    • 34249306727 scopus 로고    scopus 로고
    • N and other aspects of this computer program need further study, in our opinion.).
    • N and other aspects of this computer program need further study, in our opinion.).
  • 30
    • 51649085992 scopus 로고    scopus 로고
    • K. Cranmer, B. Mellado, W. Quayle, S.L. Wu, Statistical methods to assess the combined sensitivity of the ATLAS detector to the Higgs Boson in the standard model, ATL-PHYS-2004-034 〈http://cdsweb.cern.ch/record/726480〉; and further comments by Kyle Cranmer, private communication.
    • K. Cranmer, B. Mellado, W. Quayle, S.L. Wu, Statistical methods to assess the combined sensitivity of the ATLAS detector to the Higgs Boson in the standard model, ATL-PHYS-2004-034 〈http://cdsweb.cern.ch/record/726480〉; and further comments by Kyle Cranmer, private communication.
  • 31
    • 51649098658 scopus 로고    scopus 로고
    • J. Linnemann, Upper limits and priors, in: Talk at Workshop on Confidence Limits, Fermilab, 2000 〈http://conferences.fnal.gov/cl2k/copies/linnemann1.pdf〉.
    • J. Linnemann, Upper limits and priors, in: Talk at Workshop on Confidence Limits, Fermilab, 2000 〈http://conferences.fnal.gov/cl2k/copies/linnemann1.pdf〉.
  • 34
    • 51649126909 scopus 로고    scopus 로고
    • H.K. Kim (then a graduate student at Michigan State University), private communication to JTL.
    • H.K. Kim (then a graduate student at Michigan State University), private communication to JTL.
  • 40
    • 51649084977 scopus 로고    scopus 로고
    • Artificial case suggested by an example in Ref. [32].
    • Artificial case suggested by an example in Ref. [32].
  • 41
    • 4243421500 scopus 로고
    • CDF Collaboration The example uses a dilepton analysis
    • Abe F., et al., CDF Collaboration. Phys. Rev. Lett. 74 (1995) 2626 The example uses a dilepton analysis
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2626
    • Abe, F.1
  • 42
    • 4243435538 scopus 로고
    • D0 Collaboration
    • Abachi S., et al., D0 Collaboration. Phys. Rev. Lett. 74 (1995) 2422
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2422
    • Abachi, S.1
  • 43
    • 4244105738 scopus 로고
    • D0 Collaboration
    • Abachi S., et al., D0 Collaboration. Phys. Rev. Lett. 74 (1995) 2632
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 2632
    • Abachi, S.1
  • 44
    • 51649127659 scopus 로고    scopus 로고
    • Two artificial examples from Ref. [6].
    • Two artificial examples from Ref. [6].
  • 45
    • 51649105315 scopus 로고    scopus 로고
    • An artificial example with small τ.
    • An artificial example with small τ.
  • 48
    • 0142168116 scopus 로고    scopus 로고
    • Milagro Collaboration
    • Atkins R., et al., Milagro Collaboration. Astrophys. J. 595 (2003) 803
    • (2003) Astrophys. J. , vol.595 , pp. 803
    • Atkins, R.1
  • 49
    • 0004245694 scopus 로고
    • Abramowitz M., and Stegun I.A. (Eds), Dover, New York
    • In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions (1968), Dover, New York
    • (1968) Handbook of Mathematical Functions


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.