Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

HU HongBo; Jason Nielsen

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2000, Vol. 24> Issue(5) : 445-450

Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

HU HongBo ^, ,
Jason Nielsen

University of Wisconsin Madison, Wisconsin, USA

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Abstract：
The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only(“null”)hypothesis. A typical approach uses toy Monte Carlo experiments to build an expected experiment estimator distribution against which an observed experiment's estimator may be compared. In this note, a new approach is presented which calculates analytically the experiment estimator distribution via a Fourier transform, using the likelihood ratio as an ordering estimator. The analytic approach enjoys an enormous speed advantage over the toy Monte Carlo method, making it possible to quickly and precisely calculate confidence level results.

References

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. Janot P ,Le Diberder F .Nucl. Instrum .Methods,1998,A4 11 :449 2. Junk T .Confidence Level Computation for Combining Searches with Small Statistics.CERN –EP 99–0 4 1 and hep ex/990 2 0 0 6,1 9993. Read A L .Optimal Statistical Analysis of Search Results based on the Likelihood Ratio and its Application to the Search for the MSM Higgs Boson at s=161 and 172GeV ,DELPHI note 97—158 PHYS 737,1 9974. Obraztsov V F .Nucl. Instrum .Methods,1992 ,A31 6:388— 390 5. JINS ,Mc Namara P .The Signal Estimator Limit Setting Method ,Physics/ 981 2030 ,1998

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HU HongBo and Jason Nielsen. Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform[J]. Chinese Physics C, 2000, 24(5): 445-450.

HU HongBo and Jason Nielsen. Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform[J]. Chinese Physics C, 2000, 24(5): 445-450. shu

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Received: 1999-10-19
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

HU HongBo ^,
Jason Nielsen

Corresponding author: HU HongBo,

University of Wisconsin Madison, Wisconsin, USA

Received Date: 1999-10-19
Accepted Date: 1900-01-01
Available Online: 2000-04-05

Abstract: The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only(“null”)hypothesis. A typical approach uses toy Monte Carlo experiments to build an expected experiment estimator distribution against which an observed experiment's estimator may be compared. In this note, a new approach is presented which calculates analytically the experiment estimator distribution via a Fourier transform, using the likelihood ratio as an ordering estimator. The analytic approach enjoys an enormous speed advantage over the toy Monte Carlo method, making it possible to quickly and precisely calculate confidence level results.