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The incorporation of systematic uncertainties into confidence intervalcalculations has been addressed recently in a paper by Conrad et al. (PhysicalReview D 67 (2003) 012002). In their work, systematic uncertainities indetector efficiencies and background flux predictions were incorporatedfollowing the hybrid frequentist-Bayesian prescription of Cousins and Highland,but using the likelihood ratio ordering of Feldman and Cousins in order toproduce "unified" confidence intervals. In general, the resulting intervalsbehaved as one would intuitively expect, i.e. increased with increasinguncertainties. However, it was noted that for numbers of observed events lessthan or of order of the expected background, the intervals could sometimesbehave in a completely counter-intuitive fashion -- being seen to initiallydecrease in the face of increasing uncertainties, but only for the case ofincreasing signal efficiency uncertainty. In this comment, we show that theproblematic behaviour is due to integration over the signal efficiencyuncertainty while maximising the best fit alternative hypothesis likelihood. Ifthe alternative hypothesis likelihood is determined by unconditionallymaximising with respect to both the unknown signal and signal efficiencyuncertainty, the limits display the correct intuitive behaviour.Comment: Submitted to Physical Review

Comment on “Including systematic uncertainties in confidence interval construction for Poisson statistics”