Experimental Astronomy

, Volume 1, Issue 3, pp 145–163 | Cite as

Statistical data analysis for gamma-ray astronomy

  • S. N. Zhang
  • D. Ramsden


Significance testing, parameter estimation and sensitivity calculations for γ-ray telescopes are discussed for single ‘on-off” astronomical observations. Four widely used significance test methods are examined by Monte-Carlo simulations. The Maximum Likelihood Ratio Method is found to consistently over-estimate the significance of an observation by a few percents whereas the Fisher's Exact Test is shown to be slightly conservative and always under-estimates the significance by about the same amount when the reported significance is about 3σ and therefore it is preferred for γ-ray astronomy applications. Two methods for constructing a confidence interval and an upper limit for γ-ray source counts are discussed. It is found that the method based on the Smooth Transformation provides slightly better estimations. A new formula for the calculation of the sensitivity of a γ-ray telescope is presented, in contrast to the widely accepted one, and their statistical meanings are explained in detail.


Confidence Interval Data Analysis Parameter Estimation Likelihood Ratio Statistical Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. AnscombeF.J. (1948) Biometrika, 35, 246–254Google Scholar
  2. BestD.J. (1975) Austral. J. Statist., 17(1), 29–33Google Scholar
  3. BickelJ.P., DoksumK.A. (1977) Mathematical Statistics: Basic Ideas and Selected Topics, pp228, San Francisco: Holden-DayGoogle Scholar
  4. BrownleeK.A. (1965) Statistical Theory and Methodology in Science and Engineering (Second Edition), New York: John Wiley & SonsGoogle Scholar
  5. CherryM.L., ChuppE.L., DunphyP.P., ForrestD.J., RyanJ.M. (1980) The Astrophysical Journal, 242, 1257–1265Google Scholar
  6. D'AgostinoR.B., ChaseW., BelangerA. (1988) The American Statistician, 42(3), 198–202Google Scholar
  7. DetreK., WhiteC. (1970) Biometrics, 26, 851–854Google Scholar
  8. DowthwaiteJ.C., GibsonA.I., HarrisonA.B., KirkmanI.W., LottsA.P., MacraeJ.H., OrfordK.J., TurverK.E., WalmsleyM. (1983) Astron. Astrophys., 126, 1–6Google Scholar
  9. HastingsN.A., PeacockJ.B. (1975) Statistical Distributions, London: ButterworthsGoogle Scholar
  10. HearnD. (1969) Nucl. Instr. Methods, 70, 200Google Scholar
  11. HillierR. (1984) Gamma-Ray Astronomy, p50, Oxford: Clarendon PressGoogle Scholar
  12. HoelP.G. (1945) Ann. Math. Statist., 16, 362–368Google Scholar
  13. HuffmanM.D. (1984) Applied Statistics, 33, 224–226Google Scholar
  14. HuffmanM.D. (1985) Comm. Statist.-Theor. Meth., 14(12), 3063–3074Google Scholar
  15. LehmannE.L. (1959) Testing Statistical Hypotheses, New York: WileyGoogle Scholar
  16. LiT.P., MaY.Q. (1983) The Astrophysical Journal, 272, 317–324Google Scholar
  17. NagleD.E., GaisserT.K., ProthereoR.J. (1988) Ann. Rev. Part. Sci., 38, 609–657Google Scholar
  18. O'MongainE. (1973) Nature, 241, 376Google Scholar
  19. PrzyborowskiJ., WilenskiH. (1940) Biometrika, 31, 313–323Google Scholar
  20. ShiueW.K., BainL.J. (1982) Appl. Statist., 31(2), 130–134Google Scholar
  21. SichelH.S. (1973) Appl. Statist., 22, 50–58Google Scholar
  22. Staubert, R. (1985) Proceed. 19th Int. Cosmic Ray Conf., San Diego paper OG 9.5-10, 437Google Scholar
  23. TocherK.D. (1950) Biometrika, 38, 130–144Google Scholar
  24. UptonG.J.G. (1982) Journal of the Royal Statistical Society, Ser. A, 145, 86–105Google Scholar
  25. Wheaton, W.A., Jacobson, A.S., Ling, J.C., Mahoney, W.A. (1987) Contribution to the Workshop on Nuclear Spectroscopy of Astrophysical Sources, JPL Astrophysics Preprint, No. 88-171Google Scholar
  26. Zhang, S.N., Ramsden, D., Lloyds-Evans, J. (1989) Submitted to Experimental Astronomy Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • S. N. Zhang
    • 1
  • D. Ramsden
    • 1
  1. 1.Department of PhysicsThe University of SouthamptonSouthamptonU.K.

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