A program for confidence interval calculations for a Poisson process with background including systematic uncertainties: POLE 1.0

A Fortran 77 routine has been developed to calculate confidence intervals with and without systematic uncertainties using a frequentist confidence interval construction with a Bayesian treatment of the systematic uncertainties. The routine can account for systematic uncertainties in the background prediction and signal/background efficiencies. The uncertainties may be separately parametrized by a Gauss, log-normal or flat probability density function (PDF), though since a Monte Carlo approach is chosen to perform the necessary integrals a generalization to other parameterizations is particularly simple. Full correlation between signal and background efficiency is optional. The ordering schemes for frequentist construction currently supported are the likelihood ratio ordering (also known as Feldman-Cousins) and Neyman ordering. Optionally, both schemes can be used with conditioning, meaning the probability density function is conditioned on the fact that the actual outcome of the background process can not have been larger than the number of observed events.

Program summary

Title of program: POLE version 1.0Catalogue identifier: ADTAProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTAProgram available from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: NoneComputer for which the program is designed: DELL PC 1 GB 2.0 Ghz Pentium IVOperating system under which the program has been tested: RH Linux 7.2 Kernel 2.4.7-10Programming language used: Fortran 77Memory required to execute with typical data: ∼1.6 MbytesNo. of bytes in distributed program, including test data, etc.: 373745No. of lines in distributed program, including test data, etc.: 2700Distribution format: tar gzip fileKeywords: Confidence interval calculation, Systematic uncertaintiesNature of the physical problem: The problem is to calculate a frequentist confidence interval on the parameter of a Poisson process with known background in presence of systematic uncertainties in experimental parameters such as signal efficiency or background prediction.Method of solution: A PDF for the confidence interval construction is constructed by folding a Poisson density function with a parametrization describing the posterior PDF of the systematic uncertainties. The construction is then performed with this new PDF according to different ordering schemes. The convolution is performed using a Monte Carlo integration method, providing greatest possible flexibility with respect to the parametrization.Restriction on the complexity of the problem: No restrictions.Typical running time: for calculation of a single confidence interval with 1000 steps in signal hypothesis space the wall clock time on a DELL PC 1 GB 2.0 Ghz Pentium IV with 4 GB swap is ca. 500 seconds. The wall clock time scales roughly linear with the number of steps in signal space.Unusual features of the program: POLE uses routines from the CERNLIB library [http://wwwasd.web.cern.ch/wwwasd/cernlib], which have to be linked in during compilation. It should be noted that the number of steps in signal space (maximal s required divided by the step-width) should not exceed 1000, since the corresponding arrays are predimensioned.References: [1] J. Conrad, O. Botner, A. Hallgren, C. Perez de los Heros, Including systematic uncertainties in confidence interval construction for Poisson statistics, Phys. Rev. D 67 (2003) 012002, hep-ex/0202013.