publication . Article . Preprint . 2017

Modeling theoretical uncertainties in phenomenological analyses for particle physics

Valentin Niess; Sébastien Descotes-Genon; Jérôme Charles; Luiz Vale Silva;
Open Access English
  • Published: 01 Apr 2017
  • Publisher: HAL CCSD
  • Country: France
Abstract
International audience; The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random, nuisance, external) in the frequentist framework, and we derive the corresponding p-values. In the case of the nuisance approach where theoretical uncertainties are modeled as biases, we highlight the important, but arbitrary, issue of the range of variation chosen for the bias parameters. We introduce the concept of adaptive p-value, which is obtained by adjusting the range of variation for the bias accordin...
Subjects
free text keywords: [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph], Physics and Astronomy (miscellaneous), Engineering (miscellaneous), High Energy Physics - Phenomenology, High Energy Physics - Experiment, Physics - Data Analysis, Statistics and Probability, Astrophysics, QB460-466, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798, Metrology, Frequentist inference, Flavour, Probability and statistics, Physics, Statistical physics, Standard Model, Quark
Funded by
EC| RBI-T-WINNING
Project
RBI-T-WINNING
Ruđer Bošković Institute: Twinning for a step forward of the Theoretical Physics Division
  • Funder: European Commission (EC)
  • Project Code: 692194
  • Funding stream: H2020 | CSA
,
EC| ELUSIVES
Project
ELUSIVES
The Elusives Enterprise: Asymmetries of the Invisible Universe
  • Funder: European Commission (EC)
  • Project Code: 674896
  • Funding stream: H2020 | MSCA-ITN-ETN
,
EC| InvisiblesPlus
Project
InvisiblesPlus
InvisiblesPlus
  • Funder: European Commission (EC)
  • Project Code: 690575
  • Funding stream: H2020 | MSCA-RISE
18 references, page 1 of 2

4 Illustration of the approaches in the one-dimensional case 10 4.1 Situation of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 The random- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 The nuisance- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 The external- approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Comparison of the methods in the one-dimensional case 14 5.1 p-values and con dence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.2 Signi cance thresholds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.3 Coverage properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.4 Conclusions of the uni-dimensional case . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 Generalization to multi-dimensional cases 21 6.1 General formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6.2 Averaging measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.2.1 Averaging two measurements and the choice of a hypervolume . . . . . . . . . 22 6.2.2 Averaging n measurements with biases in a hyperball . . . . . . . . . . . . . . 24 6.2.3 Averages with other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 6.2.4 Other approaches in the literature . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.3 Global t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.3.1 Estimators and errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.4 Goodness-of- t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.5 Pull parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.6 Conclusions of the multi-dimensional case . . . . . . . . . . . . . . . . . . . . . . . . . 30 Significance (Gaussian units) 6 5 4 3 2 1 Significance (Gaussian units) 6 5 4 3 2 1 1 n [6] R. D. Cousins, J. T. Linnemann and J. Tucker, Nucl. Instrum. Meth. A 595 (2008) 480.

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