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

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