2000 character limit reached
Under-coverage in high-statistics counting experiments with finite MC samples (2401.10542v2)
Published 19 Jan 2024 in physics.data-an and hep-ex
Abstract: We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of systematic uncertainties modeled as nuisance parameters. We use the profile-likelihood ratio for statistical inference and focus on the case in which the model is determined from Monte Carlo simulated samples of finite size. We start by presenting a toy model in which the asymptotic properties of the profile-likelihood ratio are manifestly broken even if the numbers of events per bin in both the data and simulated samples are seemingly large enough to warrant their validity. We then move to the general setting to show how statistical uncertainties in the Monte Carlo predictions can affect the coverage of confidence intervals constructed in the asymptotic approximation always in the same direction, namely they lead to systematic under-coverage.
- Chirkin, D.: Likelihood description for comparing data with simulation of limited statistics. Preprint at https://doi.org/10.48550/arXiv.1304.0735 (2013) Glusenkamp [2018] Glusenkamp, T.: Probabilistic treatment of the uncertainty from the finite size of weighted monte carlo data. Eur. Phys. J. Plus 133(218) (2018) https://doi.org/10.1140/epjp/i2018-12042-x Arguelles et al. [2019] Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Glusenkamp, T.: Probabilistic treatment of the uncertainty from the finite size of weighted monte carlo data. Eur. Phys. J. Plus 133(218) (2018) https://doi.org/10.1140/epjp/i2018-12042-x Arguelles et al. [2019] Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Glusenkamp, T.: Probabilistic treatment of the uncertainty from the finite size of weighted monte carlo data. Eur. Phys. J. Plus 133(218) (2018) https://doi.org/10.1140/epjp/i2018-12042-x Arguelles et al. [2019] Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Arguelles, C.A., Schneider, A., T. Yuan: A binned likelihood for stochastic models. J. High Energ. Phys. 06(030) (2019) https://doi.org/10.1007/JHEP06(2019)030 Workman and et al. (Particle Data Group) [2020] Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Workman, R.L., (Particle Data Group) Prog. Theor. Exp. Phys. 2020(083C01) (2020) Baker and Cousins [1984] Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Baker, S., Cousins, D.: Clarification of the use of chi-square and likelihood functions in fit to histograms. Nucl. Instr. and Meth. in Phys. Research 221, 437–442 (1984) Wilks [1938] Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9(1), 60–62 (1938) Cowan [1998] Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Cowan, G. (ed.): Statistical Data Analysis. Oxford University Press, Oxford UK (1998) Cowan and et al. [2011] Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Cowan, G., al.: Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71(1554) (2011) https://doi.org/10.1140/epjc/s10052-011-1554-0 Conway [2011] Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Conway, J.S.: Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra. Proceedings of the PHYSTAT 2011, arXiv:1103.0354 [physics.data-an] (2011) Punzi [2005] Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Punzi, G.: Ordering algorithms and confidence intervals in the presence of nuisance parameters. Proceedings of PHYSTAT 2005, arXiv:physics/0511202 [physics.data-an] (2005) Kranmer [2005] Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005) Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
- Kranmer, K.S.: Frequentist Hypothesis Testing with Background Uncertainty. Proceedings of PHYSTAT 2005, arXiv:physics/0310108 [physics.data-an] (2005)
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