Some Comments on χ2 Minimisation Applications
نویسنده
چکیده
χ2 minimisation. The determination of parameters in fits to measured data is a standard task of data analysis. The standard method of least squares is often referred to as χ2 minimisation, which is a confusion in terminology; the minimum of the least squares sum follows often, but not always, the χ2 distribution. In “χ2 minimization” used in a wide range of applications from calorimeter calibration to complex analyses like fitting parton densities using data from different experiments (“. . . to determine these parameters one must minimise a χ2 which compares the measured values . . . to the calculated ones . . . .”) a variety of different non-standard concepts is used, often motivated by serious problems to handle the experimental data in a consistent way; these methods as used in recent applications may result in a bias of the fitted parameter values. Two examples showing common mistakes in the construction of χ2-expressions are discussed below. Calorimeter calibration. Calorimeters for energy measurements in a particle detector require a calibration, usually based on data taken with a fixed beam energy E. The measured data yjk for calorimeter cell j in event k (total N events) have to be related to this known energy E. A method used in many experiments is based on the minimisation of the expression
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