Numerical Computation of p-values with myFitter

Abstract

Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are, however, many realistic situations where Wilks' theorem does not apply. In particular, no simple formula exists for the comparison of models that are not nested, in the sense that one model can be obtained from the other by fixing some of its parameters. In this paper I present methods for efficient numerical computations of p-values, which work for both nested and non-nested models and do not rely on additional approximations. These methods have been implemented in a publicly available C++ framework for maximum likelihood fits called myFitter and have recently been applied in a global analysis of the Standard Model with a fourth generation of fermions.

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• Impact of a Higgs boson at a mass of 126 GeV on the standard model with three and four fermion generations
• Joint analysis of Higgs decays and electroweak precision observables in the Standard Model with a sequential fourth generation
• Status of the fourth fermion generation before ICHEP2012: Higgs data and electroweak precision observables

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• On the Statistical Treatment of the Cabibbo Angle Anomaly
• CP Violation in $D^0\to K_S{K}_S$
• Sum Rules of Charm CP Asymmetries beyond the SU(3)${}_F$ Limit
• EasyScan_HEP: a tool for connecting programs to scan the parameter space of physics models
• Nested sampling for frequentist computation: fast estimation of small $p$-values
• Fitting the Two-Higgs-Doublet model of type II