Sifting data in the real world

Abstract

In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the archives of the Particle Data Group--is a compendium of all published data, and hence, unscreened. Inspection of similar data sets quickly shows that, for many reasons, these data sets have many outliers--points well beyond what is expected from a normal distribution--thus ruling out the use of conventional $\chi^2$ techniques. This note suggests an adaptive algorithm that allows a phenomenologist to apply to the data sample a sieve whose mesh is coarse enough to let the background fall through, but fine enough to retain the preponderance of the signal, thus sifting the data. A prescription is given for finding a robust estimate of the best-fit model parameters in the presence of a noisy background, together with a robust estimate of the model parameter errors, as well as a determination of the goodness-of-fit of the data to the theoretical hypothesis. Extensive computer simulations are carried out to test the algorithm for both its accuracy and stability under varying background conditions.