paper.tex

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\title{Handling uncertainties in background shapes: the discrete profiling method}

\author{P.~D.~Dauncey$^a$\thanks{Corresponding author.},
M.~Kenzie$^b$, N.~Wardle$^b$ and G.~J.~Davies$^a$\\
\llap{$^a$}Department of Physics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK.\\
\llap{$^b$}CERN, CH-1211 Geneva 23, Switzerland.\\
E-mail: \email{P.Dauncey@imperial.ac.uk}}


\abstract{
A common problem in data analysis is that the functional form, as well as the parameter values,
of the underlying model which should describe a dataset is not known {\it a priori}. In these cases some
extra uncertainty must be assigned to the extracted parameters of interest due to lack of exact knowledge of the functional form of the model.
A method for assigning an appropriate error is presented. The method is based on
considering the choice of functional form as a discrete nuisance parameter which is
profiled in an analogous way to continuous nuisance parameters. The bias and coverage of this method are shown to be good when applied to
a realistic example.
}

\keywords{Analysis and statistical methods; Simulation methods and programs}

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\acknowledgments
We thank Chris Seez and Louis Lyons for informative discussions.
This work was partially supported by the Science and Technology Facilities
Council, UK.

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