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

Combined QCD analysis of e^+ e^- data at sqrt(s) = 14 to 172 GeV

A study of the energy dependence of event shape observables is presented. The strong coupling constant \alpha_s has been determined from the mean values of six event shape observables. Power corrections, employed for the measurement of \alpha_s, have been found to approximately account for hadronisation effects.Comment: 6 pages, uses espcrc2.sty (included) and epsfig.sty, LaTeX, 8 .eps-file

SVD Approach to Data Unfolding

Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value Decomposition (SVD) of the response matrix. A relatively simple, yet quite efficient unfolding procedure is explained in detail. The concise linear algorithm results in a straightforward implementation with full error propagation, including the complete covariance matrix and its inverse. Several improvements upon widely used procedures are proposed, and recommendations are given how to simplify the task by the proper choice of the matrix. Ways of determining the optimal value of the regularization parameter are suggested and discussed, and several examples illustrating the use of the method are presented.Comment: 22 page

Perturbative QCD description of multiparticle correlations in quark and gluon jets

The QCD evolution equations in Modified Leading Log Approximation for the factorial moments of the multiplicity distribution in quark and gluon jets are numerically solved with initial conditions at threshold by fully taking into account the energy conservation law. After applying Local Parton Hadron Duality as hadronization prescription, a consistent quantitative description of available experimental data for factorial cumulants and factorial moments of arbitrary order and for their ratio both in quark and gluon jets and in $e^+e^-$ annihilation is achieved.Comment: LaTeX, 15 pages, 3 figures, typos corrected in the labels and caption of Figure

Topology Dependence of Event Properties in Hadronic Z Decays

Three-jet events are studied for different event topologies. Experimental evidence is presented that the multiplicities of quark and gluon jets depend both on the jet energy and on the angles between the jets