Searching for new physics with profile likelihoods: Wilks and beyond

Abstract

Particle physics experiments use likelihood ratio tests extensively to compare hypotheses and to construct confidence intervals. Often, the null distribution of the likelihood ratio test statistic is approximated by a ${\chi }^2$ distribution, following a theorem due to Wilks. However, many circumstances relevant to modern experiments can cause this theorem to fail. In this paper, we review how to identify these situations and construct valid inference.

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References in corpus (9)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Observation of electron-antineutrino disappearance at Daya Bay
• Results from a search for dark matter in the complete LUX exposure
• Dark Matter Results From 54-Ton-Day Exposure of PandaX-II Experiment
• Measurement of Higgs boson production in the diphoton decay channel in $pp$ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector
• Handling uncertainties in background shapes: the discrete profiling method
• Higher-order asymptotic normality of approximations to the modified signed likelihood ratio statistic for regular models
• Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

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