Statistical Science

The Banff Challenge: Statistical Detection of a Noisy Signal

A. C. Davison and N. Sartori

Full-text: Open access

Abstract

Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability model for this and derive frequentist and noninformative Bayesian procedures for inference about the signal. Both are highly accurate in realistic cases, with the frequentist procedure having the edge for interval estimation, and the Bayesian procedure yielding slightly better point estimates. We also argue that the significance, or p-value, function based on the modified likelihood root provides a comprehensive presentation of the information in the data and should be used for inference.

Article information

Source
Statist. Sci., Volume 23, Number 3 (2008), 354-364.

Dates
First available in Project Euclid: 28 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.ss/1233153063

Digital Object Identifier
doi:10.1214/08-STS260

Mathematical Reviews number (MathSciNet)
MR2483908

Zentralblatt MATH identifier
1329.94022

Keywords
Bayesian inference higher-order asymptotics Large Hadron Collider likelihood noninformative prior orthogonal parameter particle physics Poisson distribution signal detection

Citation

Davison, A. C.; Sartori, N. The Banff Challenge: Statistical Detection of a Noisy Signal. Statist. Sci. 23 (2008), no. 3, 354--364. doi:10.1214/08-STS260. https://projecteuclid.org/euclid.ss/1233153063


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References

  • Barndorff-Nielsen, O. E. (1978). Information and Exponential Families in Statistical Theory. Wiley, New York.
  • Barndorff-Nielsen, O. E. and Cox, D. R. (1994). Inference and Asymptotics. Chapman and Hall, London.
  • Brazzale, A. R., Davison, A. C. and Reid, N. (2007). Applied Asymptotics: Case Studies in Small Sample Statistics. Cambridge Univ. Press, Cambridge.
  • Cox, D. R. (2006). Principles of Statistical Inference. Cambridge Univ. Press, Cambridge.
  • Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion). J. Roy. Statist. Soc. Ser. B 49 1–39.
  • Davison, A. C. (2003). Statistical Models. Cambridge Univ. Press, Cambridge.
  • Davison, A. C., Fraser, D. A. S. and Reid, N. (2006). Improved likelihood inference for discrete data. J. Roy. Statist. Soc. Ser. B 68 495–508.
  • Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80 27–38.
  • Fraser, D. A. S., Reid, N. and Wong, A. C. M. (2004). Inference for bounded parameters. Phys. Rev. D 69 033002.
  • O’Hagan, A. and Forster, J. J. (2004). Kendall’s Advanced Theory of Statistics. Volume 2B: Bayesian Inference, 2nd ed. Hodder Arnold, London.
  • Jeffreys, H. (1961). Theory of Probability, 3rd ed. Clarendon Press, Oxford.
  • Kosmidis, I. (2007). Bias reduction in exponential family nonlinear models. Ph.D. thesis, Dept. Statistics, Univ. Warwick.
  • Lyons, L. (2008). Open statistical issues in particle physics. Ann. Appl. Statist. 2 887–915.
  • Mandelkern, M. (2002). Setting confidence intervals for bounded parameters (with discussion). Statist. Sci. 17 149–172.
  • Pace, L. and Salvan, A. (1997). Principles of Statistical Inference from a Neo-Fisherian Perspective. World Scientific, Singapore.
  • Reid, N. (2003). Asymptotics and the theory of inference. Ann. Statist. 31 1695–1731.
  • Reid, N., Mukerjee, R. and Fraser, D. A. S. (2002). Some aspects of matching priors. In Mathematical Statistics and Applications: Festschrift for Constance van Eeden (M. Moore, S. Froda and C. Léger, eds.). Lecture Notes—Monograph Series 42 31–44. IMS, Hayward, CA.
  • Severini, T. A. (2000). Likelihood Methods in Statistics. Clarendon Press, Oxford.
  • Tibshirani, R. J. (1989). Noninformative priors for one parameter of many. Biometrika 76 604–608.
  • Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihoods. J. Roy. Statist. Soc. Ser. B 25 318–329.