Confidence intervals with a priori parameter bounds

详细信息    查看全文

• 作者：A. V. Lokhov ; F. V. Tkachov
• 刊名：Physics of Particles and Nuclei
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：46
• 期：3
• 页码：347-365
• 全文大小：577 KB
• 参考文献：1.J. Neyman, 鈥淥utline of a theory of statistical estimation based on the classical theory of probability,鈥?Phil. Trans. R. Soc. Lond. A 236, 333鈥?80 (1937).View Article ADS
  2.V. N. Aseev et al., Phys. Rev. D 84, 112003 (2011).View Article ADS
  3.H.V. Klapdor-Kleingrothaus et al., Eur. Phys. J. A 12, 147 (2001); E. Andreotti et al., Astropart. Phys. 34, 822 (2011), arXiv:1012.3266; R. Arnold et al., Nucl. Phys. A 765, 483 (2006), arXiv:hep-ex/0601021; A. Barabash et al., Phys. Atom. Nucl. 74, 312 (2011), arXiv:1002.2862.View Article ADS
  4.K. Abe et al., Phys. Rev. Lett. 107, 041801(2011), arXiv:1106.2822; P. Adamson et al., Phys. Rev. Lett. 107, 181802 (2011), arXiv:1108.0015.View Article ADS
  5.T. E. Sterne, Biometrika 41, 275 (1954); E. L. Crow, Biometrika 43, 423 (1956), E. L. Crow and R. S. Gardner, Biometrika 46, 441 (1959).MATH MathSciNet
  6.G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998).View Article ADS
  7.G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Power-Constrained Limits, arXiv:1105.3166.
  8.M. Mandelkern and J. Schultz, 鈥淭he statistical analysis of Gaussian and Poisson signals near physical boundaries,鈥?J. Math. Phys. 41, 5701鈥?709 (2000), arXiv:hep-ex/9910041v3.View Article ADS MATH MathSciNet
  9.F. Tkachov, Optimal Confidence Intervals for Bounded Parameters, arXiv:0911.4271
  10.Ch. Kraus et al., Eur. Phys. J. C 40, 447 (2005).View Article ADS
  11.V. M. Lobashev, Prog. Part. Nucl. Phys. 48, 123 (2002); Nucl. Phys. A 719,153 (2003); V. M. Lobashev et al., Nucl. Phys. B (Proc. Suppl.) 91, 280 (2001).View Article ADS
  12.F. V. Tkachov, Optimal Upper Bounds for Non-Negative Parameters, arXiv:0912.1555
  13.A. A. Tyapkin, On the interpretation of the basic problems of the estimation theory [Appendix to the Russian Translation of the Statistical Methods in Experimental Physics], Eds. by W.T. Eadie, D. Dryard, F.E. James, M. Roos, and B. Sadoulet (Atomizdat, Moscow, 1976).
  14.A. L. Read, 鈥淢odified frequentist analysis of search results (the CLs method),鈥?Proceedings of the Workshop on Confidence Limits, CERN, Switzerland, 17鈥?8 January 2000, Eds. by F. James, L. Lyons, and Y. Perrin, 2000, p. 81.
  15.鈥淭he ATLAS collaboration,鈥?Phys. Lett. B 716, 1 (2012); 鈥淭he CMS collaboration,鈥?Phys. Lett. B 716, 30 (2012).
  16.W. T. Eadie, D. Dryard, F. E. James, M. Roos, and B. Sadoulet, Statistical Methods in Experimental Physics (North-Holland, 1971).MATH
  17.F. V. Tkachov, Transcending the Least Squares, arXiv:physics/0604127.
  18.C. Giunti, Phys. Rev. D 59, 053001 (1999).View Article ADS
  19.R. D. Cousins, Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter, arXiv:1109.2023.
  20. http://鈥媤ww.鈥媔nr.鈥媋c.鈥媟u/鈥媬blackbox/鈥媠tat/鈥媔ntervals/鈥?/span>
  
• 作者单位：A. V. Lokhov (1)
  F. V. Tkachov (1)
  
  1. Institute for Nuclear Research RAS, Moscow, 117312, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Elementary Particles and Nuclei
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8559

文摘

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution of the problem. Derived are the solutions for the cases of a continuous distribution with non-negative estimated parameter and a discrete distribution, specifically a Poisson process with background. For both cases, the best upper limit is constructed that accounts for the a priori information. A table is provided with the confidence intervals for the parameter of Poisson distribution that correctly accounts for the information on the known value of the background along with the software for calculating the confidence intervals for any confidence levels and magnitudes of the background (the software is freely available for download via Internet).