Application of the Iterated Weighted Least-Squares Fit to counting experiments

Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well known fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.Comment: Accepted by NIM

Bias, variance, and confidence intervals for efficiency estimators in particle physics experiments

We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of trials is not constant but drawn from a Poisson distribution, b) the samples are weighted, c) the numbers of successes and failures have a variance which exceeds that of a Poisson process, which is the case, for example, when these numbers are obtained from a fit to mixture of signal and background events. Generalized Wilson intervals based on these variances are computed, and their coverage probability is studied. The efficiency estimators are unbiased in all considered cases, except when the samples are weighted. The standard Wilson interval is also suitable for case a). For most of the other cases, generalized Wilson intervals can be computed with closed-form expressions

Measurement of the forward energy flow in pp collisions at sqrt{s}=7 TeV with the LHCb detector

We present the results on the energy flow measured with minimum-bias data collected by the LHCb experiment in pp collisions at sqrt{s}=7 TeV for inclusive minimum-bias interactions, hard scattering processes and events with enhanced or suppressed diffractive contribution. The measurements are performed in the pseudorapidity range 1.9<\eta<4.9, which corresponds to the main detector acceptance of the LHCb spectrometer. The data are compared to predictions given by the PYTHIA-based and cosmic-ray Monte Carlo event generators, which model the underlying event activity in different ways

Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk Flow, Shear and Octupole Moments

The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal ``minimum variance'' (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here we extend this MV analysis to include the shear and octupole moments, which are designed to have almost no correlations between them so that they are virtually orthogonal. We apply this MV analysis to a compilation of all major peculiar velocity surveys, consisting of 4536 measurements. Our estimate of the BF on scales of ~ 100 Mpc/h has a magnitude of |v|= 416 +/- 78 km/s towards Galactic l = 282 degree +/- 11 degree and b = 6 degree +/- 6 degree. This result is in disagreement with LCDM with WMAP5 cosmological parameters at a high confidence level, but is in good agreement with our previous MV result without an orthogonality constraint, showing that the shear and octupole moments did not contaminate the previous BF measurement. The shear and octupole moments are consistent with WMAP5 power spectrum, although the measurement noise is larger for these moments than for the BF. The relatively low shear moments suggest that the sources responsible for the BF are at large distances.Comment: 13 Pages, 7 figures, 4 tables. Some changes to reflect the published versio

Hadron cascades in CORSIKA 8

We present characteristics of hadronic cascades from interactions of cosmic rays in the atmosphere, simulated by the novel CORSIKA 8 framework. The simulated spectra of secondaries, such as pions, kaons, baryons and muons, are compared with the cascade equations solvers MCEq in air shower mode, and full 3D air shower Monte Carlo simulations using the legacy CORSIKA 7. A novel capability of CORSIKA 8 is the simulation of cascades in media other than air, widening the scope of potential applications. We demonstrate this by simulating cosmic ray showers in the Mars atmosphere, as well as simulating a shower traversing from air into water. The CORSIKA 8 framework demonstrates good accuracy and robustness in comparison with previous results, in particular in those relevant for the production of muons in air showers. Furthermore, the impact of forward ρ$^{0}$ production on air showers is studied and illustrated