dorsal/arxiv
View SchemaA Unified Approach to the Classical Statistical Analysis of Small Signals
| Authors | Gary J. Feldman, Robert D. Cousins |
|---|---|
| Categories | |
| ArXiv ID | physics/9711021 |
| URL | https://arxiv.org/abs/physics/9711021 |
| DOI | 10.1103/PhysRevD.57.3873 |
| Journal | Phys.Rev.D57:3873-3889,1998 |
Abstract
We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not previously recognized) that the choice of upper limit or two-sided intervals leads to intervals which are not confidence intervals if the choice is based on the data. We apply the construction to two related problems which have recently been a battle-ground between classical and Bayesian statistics: Poisson processes with background, and Gaussian errors with a bounded physical region. In contrast with the usual classical construction for upper limits, our construction avoids unphysical confidence intervals. In contrast with some popular Bayesian intervals, our intervals eliminate conservatism (frequentist coverage greater than the stated confidence) in the Gaussian case and reduce it to a level dictated by discreteness in the Poisson case. We generalize the method in order to apply it to analysis of experiments searching for neutrino oscillations. We show that this technique both gives correct coverage and is powerful, while other classical techniques that have been used by neutrino oscillation search experiments fail one or both of these criteria.
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"abstract": "We give a classical confidence belt construction which unifies the treatment\nof upper confidence limits for null results and two-sided confidence intervals\nfor non-null results. The unified treatment solves a problem (apparently not\npreviously recognized) that the choice of upper limit or two-sided intervals\nleads to intervals which are not confidence intervals if the choice is based on\nthe data. We apply the construction to two related problems which have recently\nbeen a battle-ground between classical and Bayesian statistics: Poisson\nprocesses with background, and Gaussian errors with a bounded physical region.\nIn contrast with the usual classical construction for upper limits, our\nconstruction avoids unphysical confidence intervals. In contrast with some\npopular Bayesian intervals, our intervals eliminate conservatism (frequentist\ncoverage greater than the stated confidence) in the Gaussian case and reduce it\nto a level dictated by discreteness in the Poisson case. We generalize the\nmethod in order to apply it to analysis of experiments searching for neutrino\noscillations. We show that this technique both gives correct coverage and is\npowerful, while other classical techniques that have been used by neutrino\noscillation search experiments fail one or both of these criteria.",
"arxiv_id": "physics/9711021",
"authors": [
"Gary J. Feldman",
"Robert D. Cousins"
],
"categories": [
"physics.data-an",
"hep-ex"
],
"doi": "10.1103/PhysRevD.57.3873",
"journal_ref": "Phys.Rev.D57:3873-3889,1998",
"title": "A Unified Approach to the Classical Statistical Analysis of Small Signals",
"url": "https://arxiv.org/abs/physics/9711021"
},
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