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Manuscript Title: A program for confidence interval calculations for a Poisson process with background including systematic uncertainties: POLE 1.0.
Authors: J. Conrad
Program title: pole version 1.0
Catalogue identifier: ADTA
Journal reference: Comput. Phys. Commun. 158(2004)117
Programming language: Fortran 77.
Computer: DELL PC, 1 GB 2 Ghz Pentium IV.
Operating system: RH linux 7.2 Kernal 2.4.7-10.
RAM: 1M words
Keywords: Confidence interval calculation, Systematic uncertainties, General purpose, Statistical methods.
Classification: 4.13.

Nature of problem:
The problem is to calculate a frequentist confidence interval on the parameter of a Poisson process with known background in the presence of systematic uncertainties in experimental parameters such as signal efficiency or background prediction.

Solution method:
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.

Unusual features:
POLE uses routines from the CERNLIB library 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.

Running time:
For the calculation of a single confidence interval with 1000 steps in signal hypothesis space the wall clock time on a DELL PC 1GB 2.0 Ghz Pentium IV with 4 GB swap is ca. 500 seconds. The wall clock time scales roughly linearly with the number of steps in signal space.