Confidence intervals for linear combinations of Poisson observations

Different situations in HEP data analysis involve the calculation of confidence intervals for quantities derived as linear combinations of observations that follow a Poisson law. Although apparently a simple problem, no precise methods exist when asymptotic approximations are not accurate. Existing procedures are reviewed, and new approaches are proposed. Their performance and range of validity is checked in different benchmarks. In general, the simple methods based on error propagation or application of Wilks theorem to MLE show important undercoverage or overcoverage for low number of counts. On the contrary, methods based in profiling the likelihood or projecting the multidimensional confidence regions obtained with the Neyman construction show a much better performance. XIII Quark Confinement and the Hadron Spectrum Confinement2018 31 July 6 August 2018 Maynooth University, Ireland