The Annals of Applied Statistics

Open statistical issues in Particle Physics

Louis Lyons

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Many statistical issues arise in the analysis of Particle Physics experiments. We give a brief introduction to Particle Physics, before describing the techniques used by Particle Physicists for dealing with statistical problems, and also some of the open statistical questions.

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Ann. Appl. Stat., Volume 2, Number 3 (2008), 887-915.

First available in Project Euclid: 13 October 2008

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Particle Physics parameter determination goodness of fit p-values hypothesis testing nuisance parameters upper limits blind analysis signal-background separation combining results


Lyons, Louis. Open statistical issues in Particle Physics. Ann. Appl. Stat. 2 (2008), no. 3, 887--915. doi:10.1214/08-AOAS163.

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  • Aslan, B. and Zech, G. (2004). A multivariate two-sample test based on the concept of minimum energy. J. Stat. Comp. Simul. 75 109.
  • Aslan, B. and Zech, G. (2005). Statistical energy as a tool for binning-free multivariate goodness of fit tests, two-sample comparison and unfolding. Nuclear Instruments and Methods A537 626.
  • Belikov, J. (2007). ALICE statistical wish-list. Available at
  • CDF Statistics Committee (2007). Frequently asked questions. Available at
  • Cheung, H. and Lyons, L. (2000). FNAL confidence limits workshop. Available at
  • Cousins, R. (1998). Improved central confidence intervals for the ratio of Poisson means. Nuclear Instruments and Methods A417 391–399.
  • Cousins, R. (2007). Annotated bibliography on some papers on combining significances or p-values. Available at arXiv:0705.2209.
  • Cousins, R. D. and Highland, V. L. (1992). Incorporating systematic uncertainties into an upper limit. Nuclear Instruments and Methods A320 331.
  • Cox, D. R. (1958). Some problems connected with statistical inference. Ann. Math. Statist. 29 357–372.
  • Cranmer, K. (2007). Progress, challenges and future of statistics at the LHC. Available at
  • Cuadras, C. M., Fortiana, J. and Oliva, F. (1997). The proximity of an individual to a population with applications to discriminant analysis. J. Classification 14 117–136.
  • Cuadras, C. M. and Fortiana, J. (2003). Distance-based multivariate two sample tests. Available at
  • Demortier, L. (2005). Bayesian reference analysis. Available at
  • Demortier, L. (2006). Setting the scene for p-values. Available at 2006/06w5054/report06w5054.pdf.
  • Demortier, L. (2007). P-values and nuisance parameters. Available at
  • Drton, M. (2007). Likelihood ratio tests and singularities. Available at
  • Feldman, G. J. and Cousins, R. D. (1998). Unified approach to the classical statistical analysis of small signals. Phys. Rev. D 57 3873–3889.
  • Friedman, J. H. (2003). Recent advances in predictive (machine) learning. Available at
  • Friedman, J. H. (2005). Separating signal from background using ensembles of rules. Available at
  • Gross, E. (2007). ATLAS and CMS statistical wish-list. Available at
  • Heinrich, J. (2003a). Coverage of error bars for Poisson data. Available at
  • Heinrich, J. (2003b). Pitfalls of goodness-of-fit from likelihood. Available at
  • Heinrich, J. (2005). The Bayesian approach to setting limits: What to avoid. Available at
  • Heinrich, J. (2007). Review of Banff challenge on upper limits. Available at
  • Heinrich, J. and Lyons, L. (2007). Systematic errors. Annual Reviews of Nuclear and Particle Science 57 145–169.
  • Heinrich, J. et al. (2004). Interval estimation in the presence of nuisance parameters. 1. Bayesian approach. CDF Note 7117. Available at
  • Höcker, A. et al. (2007). TMVA—Toolkit for multivariate data analysis. Available at
  • James, F., Lyons, L. and Perrin, Y. (2000). Workshop on confidence limits. CERN Yellow Report 2000-05.
  • Klein, J. R. and Roodman, A. (2005). Blind analysis in nuclear and particle physics. Annual Review of Nuclear and Particle Physics 55 141.
  • Linnemann, J. (2007). A pitfall in evaluating systematic errors. Available at
  • Lyons, L. (1999). Comparing two hypotheses. Available at
  • Lyons, L. (2008). Supplement to “Open statistical issues in particle physics.” DOI: 10.1214/08-AOAS163SUPP.
  • Lyons, L., Martin, A. and Saxon, D. (1990). On the determination of the B lifetime by combining the results of different experiments. Phy. Rev. D 41 982.
  • Lyons, L., Mount, R. and Reitmeyer, R., eds. (2003). PHYSTAT 20003. eConf C030908, SLAC-R-703. Available at
  • Lyons, L. and Ünel, M. K. (2005). Statistical problems in particle physics, astrophysics and cosmology. Imperial College Press, London. Available at
  • Narsky, I. (2000). Comparison of upper limits. Available at
  • Narsky, I. (2006). StatPatternRecognition: A C++ package for multi-variate classification. Available at
  • Neal, R. (2007). Computing likelihood functions when distributions are defined by simulators with nuisance parameters. Available at
  • Nicolo, D. and Signorelli, G. (2002). Application of strong confidence to the CHOOZ experiment with frequentist inclusion of nuisance parameters. Available at
  • Particle Data Group (2006). J. Phys. G: Nucl. Part. Phys. 33 1 (see page 14).
  • Prosper, H. B. (2002). Multivariate analysis: A unified perspective. Available at
  • Prosper, H. B., Lyons, L. and De Roeck, A. (2007). PHYSTAT-LHC Workshop at CERN on Statistical Issues for LHC Physics. Available at
  • Protassov, R. et al. (2002). Statistics: Handle with care. Detecting multiple model components with the likelihood ratio test. Astrophysics J. 571 545–559.
  • Punzi, G. (2003). Sensitivity of searches for new signals and its optimization. Available at
  • Punzi, G. (2005). Ordering algorithms and confidence intervals in the presence of nuisance parameters. Available at
  • Read, A. L. (2000). Modified frequentist analysis of search results (the CLs method). Available at
  • Read, A. L. (2004). Presentation of search results—the CLs method. J. Phys. G: Nucl. Part. Phys. 28 2693–2704.
  • Reid, N. (2007). Some aspects of design of experiments. Available at
  • Reid, N., Linnemann, J. and Lyons, L. (2006). Workshop on statistical inference problems in high energy physics and astronomy. Available at
  • Roe, B. P. (2007). Statistical errors in Monte Carlo estimates of systematic errors. Nuclear Instruments and Methods A570 159–164.
  • Rolke, W. A., Lopez, A. M. and Conrad, J. (2005). Limits and confidence intervals in the presence of nuisance parameters. Nuclear Instruments and Methods A551 493–503.
  • Self, S. G. and Liang, K. Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio test under non-standard conditions. J. Amer. Statist. Assoc. 82 605–610.
  • Sen, B., Walker, M. and Woodroofe, M. (2008). On the unified method with nuisance parameters. Statist. Sinica. To appear.
  • Trotta, R. (2008). Bayes in the sky: Bayesian inference and model selection in cosmology. Contemporary Physics 49 71–104.
  • Whalley, M. and Lyons, L., eds. (2002). Advanced statistical techniques in particle physics, Durham IPPP/02/39. Available at
  • Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Statist. 9 60–62.
  • Xie, Y. (2007). LHCb statistical wishlist. Available at

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