Errors on Errors: Refining Statistical Analyses for Particle Physics

by Prof. Glen Cowan

Main Auditorium (Max Planck Institute for Physics)

Main Auditorium

Max Planck Institute for Physics

Föhringer Ring 6 80805 München

In a statistical analysis in Particle Physics, one faces two distinct challenges: the limited number of particle collisions and imperfections in the modelling of the events produced. Roughly speaking these correspond to "statistical" and "systematic" errors in the result. To help combat the systematic uncertainties one can try to improve the statistical model by including additional (nuisance) parameters. The best estimate of such a parameter is often treated as a Gaussian distributed variable with a given standard deviation. The appropriate values for these standard deviations are, however, often the subject of heated argument, which is to say that the errors themselves have errors. A type of model is presented where the uncertainty in the assigned systematic errors is taken into account. Estimates of the systematic variances are modeled as gamma distributed variables. The resulting confidence intervals show interesting and useful properties. For example, when averaging measurements to estimate their mean, the size of the confidence interval increases as a for decreasing goodness-of-fit, and averages have reduced sensitivity to outliers. The basic properties of the model are presented and several types of examples relevant for Particle Physics are explored.

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