Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

HU HongBo; Jason Nielsen

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]	ZHANG Chao , ZHENG Xiao-Ping . Kinetic-Theory Approach to the “Hard Thermal Loop” Self-Energy Including Chemical Potential. Chinese Physics C, 2003, 27(1): 63-66.
[2]	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.
[3]	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.
[4]	WEI Shi , LIN Yu-Zheng . Accurate Computation on High Order Modes of Axial-symmetric Cavity with Vector Finite Element Method. Chinese Physics C, 2001, 25(10): 1017-1021.
[5]	NI GuangJiong , WANG HaiBin , YAN Jun , LI HaiLong . Lamb Shift Calculated by a Semiquantitative Method. Chinese Physics C, 2000, 24(5): 400-407.
[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]	Liu Beishu , Zheng Xite . Analytical Calculation of Lattice SU(2)-Higgs Model with Varied Length. Chinese Physics C, 1995, 19(12): 1090-1095.
[8]	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.
[9]	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.
[10]	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.
[11]	NI Guang-Jiong , ZHANG Min , GONG Jia-Wen . A Rigorous Method for Calculating the Casimir Effect. Chinese Physics C, 1991, 15(8): 695-700.
[12]	BAI Zhi-Ming , JIANG Yuan-Fang . The One Loop Calculation of the Strong coupling β Function in the Toy Model. Chinese Physics C, 1991, 15(3): 213-219.
[13]	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.
[14]	SHEN Qing-Biao , TIAN Ye , LI Zhu-Xia , ZHUO Yi-Zhong . CALCULATION OF WIDTHS, SPECTRAL FUNCTION AND HOLE OCCUPATION NUMBERS OF SINGLE-PARTICLE STATES. Chinese Physics C, 1985, 9(3): 327-331.
[15]	LU Jing-Xian . A METHOD FOR CALCULATING PHOTON STRUCTURE FUNCTION IN DEEP INELASTIC SCATTERING. Chinese Physics C, 1985, 9(6): 697-702.
[16]	WANG Xing-Min . THE FEYNMAN RULES OF COLLECTIVE BAG-QUARK CURRENT AND HADRON TIME-LIKE STRUCTURE FUNCTIONS. Chinese Physics C, 1984, 8(2): 148-157.
[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(2746)
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.