Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

HU HongBo; Jason Nielsen

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《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

Abstract
HTML
Reference
Related

PDF

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

[1]

. 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

[1]	ZHENG Kai , WANG Jun-Hua , LIU Zu-Ping , LI Wei-Min , SUN Bao-Gen , LIU Jian-Hong , YANG Yong-Liang , ZHOU Ze-Ran , CHEN Yuan-Bo , HUANG Long-Jun . Application of Hilbert-Transform-Phase-Space-Reconstruction in HLS Bunch-by-Bunch System. Chinese Physics C, 2007, 31(3): 307-310.
[2]	MA Tian-Yu , JIN Yong-Jie . Analytical System Modeling Method for SPECT Based on the Boltzmann Transport Equation. Chinese Physics C, 2006, 30(8): 806-811.
[3]	ZHANG Shi-Sheng , MENG Jie , GUO Jian-You . Method of the Analytical Continuation of the Coupling Constant in Schrodinger Equations. Chinese Physics C, 2003, 27(12): 1095-1099.
[4]	FAN Sheng , YAN Fang , ZHANG Hong-Zhou , ZHAO Zhi-Xiang . A New Semiempirical Expression of Excitation Function for (n,p) Reaction. Chinese Physics C, 2003, 27(11): 1009-1014.
[5]	Ren Xuezao , Chen Ying , Zhu Yunlun . Analytical Study of Lattice U(1) Gauge-Higgs ModelsWith Fixed Modulus. Chinese Physics C, 1998, 22(4): 315-321.
[6]	Hui Ping . Fifth Order Approximate Analytic Calculation of (2+1)-D SU(2) Vacuum Wavefunction. Chinese Physics C, 1998, 22(4): 322-325.
[7]	Hui Ping , Cai Pengfei , Chen Qizhou . Analytic calculation of Glueball Mass In (2+1)-D SU(2)Lattice Gauge Theory. Chinese Physics C, 1996, 20(1): 55-60.
[8]	Gao Xiaochun , Gao Jun , Fu Jian . Invariant-Related Unitary Transformation Method and Evolution of the Third-Quantized Wave Function of the Universe. Chinese Physics C, 1996, 20(3): 226-233.
[9]	Liu Beishu , Zheng Xite . Analytical Calculation of Lattice SU(2)-Higgs Model with Varied Length. Chinese Physics C, 1995, 19(12): 1090-1095.
[10]	Zheng Xite , Chen Hong , Lu Zao , He Yuan . Analytical Calculation of the Fixed Length Lattice SU(2)-Higgs Model. Chinese Physics C, 1995, 19(2): 137-142.
[11]	Hui Ping , Chen Qizhou . Fourth Order Approximate Analytic Calculation of (2+1)-D SU(2) Vacuum Wavefunction. Chinese Physics C, 1995, 19(9): 820-825.
[12]	Ye Shuwei , Chen Hongfang , Wu Jian , Zhang Ziping , Niu Hongquan , Xu Tong , Tong Guoliang , LV Feng , Li Yong , Zeng Jiyang , Wu Yigen , Yi Kai , Chen Xiangyang , Xu Mi . Relative Likelihood and e/π Separation at BES. Chinese Physics C, 1995, 19(12): 1072-1077.
[13]	Lin Hai , Zhang Yang , Liu Lianshou . The Refinement of α Model and the Analytical Calculation of Levy Exponent. Chinese Physics C, 1994, 18(9): 858-864.
[14]	MAO Nai-Feng , LI Zeng-Hai . SPLINE FUNCTION REPRESENTATION FOR TRANSFORMATION OF PHASE SPACE WITH ARBITRARY CONTOURS. Chinese Physics C, 1989, 13(5): 445-450.
[15]	BAO Cheng-Guang , WANG Wei-Wei . CALCULATIONS OF THE HYPERSPHERICAL TRANSFORMATION BRACKETS OF 4-BODY SYSTEMS BY USING THOSE OF THEIR SUBSYSTEMS. Chinese Physics C, 1988, 12(4): 568-572.
[16]	LU Jing-Xian . A METHOD FOR CALCULATING PHOTON STRUCTURE FUNCTION IN DEEP INELASTIC SCATTERING. Chinese Physics C, 1985, 9(6): 697-702.
[17]	FENG Ren-Fa , ZHUO Yi-Zhong , LI Jun-Qing . ANALYTICAL MODEL FOR THE CALCULATION OF FISSION RATE. Chinese Physics C, 1984, 8(4): 453-460.
[18]	SHEN Qi-Xing , WU Ji-Min , LU Jing-Xian , ZHAO Pei-Ying . A METHOD FOR DIRECTLY COMPUTING QCD PREDICTION FOR VALENCE QUARK DISTRIBUTION FUNCTION OF THE HADRONS IN A REASONABLE APPROXIMATION. Chinese Physics C, 1983, 7(2): 170-177.
[19]	CHEN JIN-QUAN , GAO MEI-JUAN , WANG FAN . ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SU_n BARYON AND MESON WAVE FUNCTIONS. Chinese Physics C, 1979, 3(4): 408-417.
[20]	LI TI-PEI . CONFIDENCE DENSITY METHOD FOR PARAMETER ESTIMATION. Chinese Physics C, 1978, 2(2): 131-142.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(2688)
PDF Downloads(528)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.