Comment on "Including Systematic Uncertainties in Confidence Interval Construction for Poisson Statistics"

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.Comment: Submitted to Physical Review

Treatment of the background error in the statistical analysis of Poisson processes

The formalism that allows to take into account the error sigma_b of the expected mean background b in the statistical analysis of a Poisson process with the frequentistic method is presented. It is shown that the error sigma_b cannot be neglected if it is not much smaller than sqrt(b). The resulting confidence belt is larger that the one for sigma_b=0, leading to larger confidence intervals for the mean mu of signal events.Comment: 15 pages including 2 figures, RevTeX. Final version published in Phys. Rev. D 59 (1999) 11300

Plotting the Differences Between Data and Expectation

This article proposes a way to improve the presentation of histograms where data are compared to expectation. Sometimes, it is difficult to judge by eye whether the difference between the bin content and the theoretical expectation (provided by either a fitting function or another histogram) is just due to statistical fluctuations. More importantly, there could be statistically significant deviations which are completely invisible in the plot. We propose to add a small inset at the bottom of the plot, in which the statistical significance of the deviation observed in each bin is shown. Even though the numerical routines which we developed have only illustration purposes, it comes out that they are based on formulae which could be used to perform statistical inference in a proper way. An implementation of our computation is available at https://github.com/dcasadei/psde .Comment: 10 pages, 7 figures. CODE: https://github.com/dcasadei/psd

A straw drift chamber spectrometer for studies of rare kaon decays

We describe the design, construction, readout, tests, and performance of planar drift chambers, based on 5 mm diameter copperized Mylar and Kapton straws, used in an experimental search for rare kaon decays. The experiment took place in the high-intensity neutral beam at the Alternating Gradient Synchrotron of Brookhaven National Laboratory, using a neutral beam stop, two analyzing dipoles, and redundant particle identification to remove backgrounds

Do Cosmological Perturbations Have Zero Mean?

A central assumption in our analysis of cosmic structure is that cosmological perturbations have zero ensemble mean. This property is one of the consequences of statistically homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which perturbations have non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and is thus rather generic and model-independent. The test statistic we employ is essentially Student's t statistic, applied to appropriately masked, foreground-cleaned cosmic microwave background anisotropy maps produced by the WMAP mission. We find evidence for a non-zero mean in a particular range of multipoles, but the evidence against the zero mean hypothesis goes away when we correct for multiple testing. We also place constraints on the mean of the temperature multipoles as a function of angular scale. On angular scales smaller than four degrees, a non-zero mean has to be at least an order of magnitude smaller than the standard deviation of the temperature anisotropies.Comment: 31 pages, 4 tables, 6 figure

Search for flavor-changing neutral currents and lepton-family-number violation in two-body D0 decays

Results of a search for the three neutral charm decays, D0 -> mu e, D0 -> mu mu, and D0 -> e e, are presented. This study was based on data collected in Experiment 789 at the Fermi National Accelerator Laboratory using 800 GeV/c proton-Au and proton-Be interactions. No evidence is found for any of the decays. Upper limits on the branching ratios, at the 90% confidence level, are obtained.Comment: 28 pages, 18 figures. Submitted to Physical Review

Limits to the muon flux from WIMP annihilation in the center of the Earth with the AMANDA detector

A search for nearly vertical up-going muon-neutrinos from neutralino annihilations in the center of the Earth has been performed with the AMANDA-B10 neutrino detector. The data sample collected in 130.1 days of live-time in 1997, ~10^9 events, has been analyzed for this search. No excess over the expected atmospheric neutrino background is oberved. An upper limit at 90% confidence level on the annihilation rate of neutralinos in the center of the Earth is obtained as a function of the neutralino mass in the range 100 GeV-5000 GeV, as well as the corresponding muon flux limit.Comment: 14 pages, 11 figures. Version accepted for publication in Physical Review

Search for the Decay τ−→4pi−3π+(π0)ντ\tau^{-}\to 4pi^{-}3\pi^{+}(\pi^{0})\nu_{\tau}

We have searched for the decay of the tau lepton into seven charged particles and zero or one pi0. The data used in the search were collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of 4.61 fb^(-1). No evidence for a signal is found. Assuming all the charged particles are pions, we set an upper limit on the branching fraction, B(tau- -> 4pi- 3pi+ (pi0) nu_tau) < 2.4 x 10^(-6) at the 90% confidence level. This limit represents a significant improvement over the previous limit.Comment: 9 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN