arXiv: Data Analysis, Statistics and Probability, 2000
We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson dist... more We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate where the mean is the sum of a known background and an unknown non-negative signal. We point out that the intervals do not have coverage in the usual sense but can be made to have such with a modification that does not affect the believability and other desirable features of this attractive construction. A similar modification can be used to provide coverage to the construction recently proposed by Cousins for the Gaussian-with-boundary problem.
We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson dist... more We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate, where the mean is the sum of a known background and an unknown non-negative signal. The RW construction is based on a conditional pdf and posseses conditional coverage such that the intervals contain the true value of the signal with prescribed probability only for subsets of the full set of repeated experiments. The intervals do not have coverage in the usual sense but can be made to have such with a modification that does not affect the believability and other desirable features of this attractive construction. A similar modification can be used to provide coverage to a recently discussed application of this method to the gaussian-with-boundary problem. In both cases the result is equivalent to a construction in which the defining contour is the bayesian upper limit (uniform prior) for observations near the physical bound and the bayesian (or frequentist) central confidence interval asymptotically.
We propose a construction of frequentist confidence intervals that is effective near unphysical r... more We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the pathologies that affect the likelihood ratio and related constructions. Away from nonphysical regions, the results are exactly the usual central two-sided intervals. The construction is based on including the physical constraint in the derivation of the estimator, leading to an estimator with values that are confined to the physical domain.
Cross-section limits are presented for proton-antiproton annihilation into all possible four-kaon... more Cross-section limits are presented for proton-antiproton annihilation into all possible four-kaon final states in the region from threshold to 1.1 GeV/ c lab momentum. Comparisons are made with cross sections for other four-body final states. It is shown that, based on phase-space considerations, the four-- neutral-kaon final state manifests an anomalously high relative rate, suggesting the possible influence of a threshold enhancement.
arXiv: Data Analysis, Statistics and Probability, 2000
We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson dist... more We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate where the mean is the sum of a known background and an unknown non-negative signal. We point out that the intervals do not have coverage in the usual sense but can be made to have such with a modification that does not affect the believability and other desirable features of this attractive construction. A similar modification can be used to provide coverage to the construction recently proposed by Cousins for the Gaussian-with-boundary problem.
We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson dist... more We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate, where the mean is the sum of a known background and an unknown non-negative signal. The RW construction is based on a conditional pdf and posseses conditional coverage such that the intervals contain the true value of the signal with prescribed probability only for subsets of the full set of repeated experiments. The intervals do not have coverage in the usual sense but can be made to have such with a modification that does not affect the believability and other desirable features of this attractive construction. A similar modification can be used to provide coverage to a recently discussed application of this method to the gaussian-with-boundary problem. In both cases the result is equivalent to a construction in which the defining contour is the bayesian upper limit (uniform prior) for observations near the physical bound and the bayesian (or frequentist) central confidence interval asymptotically.
We propose a construction of frequentist confidence intervals that is effective near unphysical r... more We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the pathologies that affect the likelihood ratio and related constructions. Away from nonphysical regions, the results are exactly the usual central two-sided intervals. The construction is based on including the physical constraint in the derivation of the estimator, leading to an estimator with values that are confined to the physical domain.
Cross-section limits are presented for proton-antiproton annihilation into all possible four-kaon... more Cross-section limits are presented for proton-antiproton annihilation into all possible four-kaon final states in the region from threshold to 1.1 GeV/ c lab momentum. Comparisons are made with cross sections for other four-body final states. It is shown that, based on phase-space considerations, the four-- neutral-kaon final state manifests an anomalously high relative rate, suggesting the possible influence of a threshold enhancement.
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