Trial factors for the look elsewhere effect in high energy physics
Open Access
Special Article - Tools for Experiment and Theory- First Online:
- Received:
- Revised:
- 94 Citations
- 740 Downloads
Abstract
When searching for a new resonance somewhere in a possible mass range, the significance of observing a local excess of events must take into account the probability of observing such an excess anywhere in the range. This is the so called “look elsewhere effect”. The effect can be quantified in terms of a trial factor, which is the ratio between the probability of observing the excess at some fixed mass point, to the probability of observing it anywhere in the range. We propose a simple and fast procedure for estimating the trial factor, based on earlier results by Davies. We show that asymptotically, the trial factor grows linearly with the (fixed mass) significance.
Download
to read the full article text
References
- 1.L. Lyons, Open statistical issues in particle physics. Ann. Appl. Stat. 2(3), 887–915 (2008) MATHCrossRefMathSciNetGoogle Scholar
- 2.L. Demortier, P Values and nuisance parameters, in Proceedings of PHYSTAT-LHC Workshop (2007). CERN–2008–001 Google Scholar
- 3.R.B. Davies, Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247–254 (1977) MATHCrossRefMathSciNetGoogle Scholar
- 4.R.B. Davies, Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33–43 (1987) MATHMathSciNetGoogle Scholar
- 5.S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938) MATHCrossRefGoogle Scholar
- 6.CMS Physics TDR, Volume II, Appendix A.2. J. Phys. G, Nucl. Part. Phys. 34, 995–1579 (2007) Google Scholar
- 7.H. Chernoff, On the distribution of the likelihood ratio. Ann. Math. Stat. 25, 573–578 (1954) MATHCrossRefMathSciNetGoogle Scholar
- 8.W. Quayle, Combining channels with fits. Talk given at the PHYSTAT-LHC Workshop (2007). Available at http://phystat-lhc.web.cern.ch/phystat-lhc/program.html
- 9.Banff International Research Station Workshop on Statistical issues relevant to significance of discovery claims (2010). Workshop site: http://www.birs.ca/events/2010/5-day-workshops/10w5068. Luc Demortier summary talk: http://www.stat.sfu.ca/lockhart/richard/banff2010/demortier.pdf
Copyright information
© The Author(s) 2010