dorsal/arxiv
View SchemaComment on "Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics"
| Authors | Gary C. Hill |
|---|---|
| Categories | |
| ArXiv ID | physics/0302057 |
| URL | https://arxiv.org/abs/physics/0302057 |
| DOI | 10.1103/PhysRevD.67.118101 |
| Journal | Phys.Rev. D67 (2003) 118101 |
Abstract
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector efficiencies and background flux predictions were incorporated following the hybrid frequentist-Bayesian prescription of Cousins and Highland, but using the likelihood ratio ordering of Feldman and Cousins in order to produce "unified" confidence intervals. In general, the resulting intervals behaved as one would intuitively expect, i.e. increased with increasing uncertainties. However, it was noted that for numbers of observed events less than or of order of the expected background, the intervals could sometimes behave in a completely counter-intuitive fashion -- being seen to initially decrease in the face of increasing uncertainties, but only for the case of increasing signal efficiency uncertainty. In this comment, we show that the problematic behaviour is due to integration over the signal efficiency uncertainty while maximising the best fit alternative hypothesis likelihood. If the alternative hypothesis likelihood is determined by unconditionally maximising with respect to both the unknown signal and signal efficiency uncertainty, the limits display the correct intuitive behaviour.
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"abstract": "The incorporation of systematic uncertainties into confidence interval\ncalculations has been addressed recently in a paper by Conrad et al. (Physical\nReview D 67 (2003) 012002). In their work, systematic uncertainities in\ndetector efficiencies and background flux predictions were incorporated\nfollowing the hybrid frequentist-Bayesian prescription of Cousins and Highland,\nbut using the likelihood ratio ordering of Feldman and Cousins in order to\nproduce \"unified\" confidence intervals. In general, the resulting intervals\nbehaved as one would intuitively expect, i.e. increased with increasing\nuncertainties. However, it was noted that for numbers of observed events less\nthan or of order of the expected background, the intervals could sometimes\nbehave in a completely counter-intuitive fashion -- being seen to initially\ndecrease in the face of increasing uncertainties, but only for the case of\nincreasing signal efficiency uncertainty. In this comment, we show that the\nproblematic behaviour is due to integration over the signal efficiency\nuncertainty while maximising the best fit alternative hypothesis likelihood. If\nthe alternative hypothesis likelihood is determined by unconditionally\nmaximising with respect to both the unknown signal and signal efficiency\nuncertainty, the limits display the correct intuitive behaviour.",
"arxiv_id": "physics/0302057",
"authors": [
"Gary C. Hill"
],
"categories": [
"physics.data-an"
],
"doi": "10.1103/PhysRevD.67.118101",
"journal_ref": "Phys.Rev. D67 (2003) 118101",
"title": "Comment on \"Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics\"",
"url": "https://arxiv.org/abs/physics/0302057"
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