Abstract
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable with a given standard deviation (the corresponding “systematic error”). Although the assigned systematic errors are usually treated as constants, in general they are themselves uncertain. 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 random 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 for decreasing goodness-of-fit, and averages have reduced sensitivity to outliers. The basic properties of the model are presented and several examples relevant for Particle Physics are explored.
Highlights
Data analysis in Particle Physics is based on observation of a set of numbers that can be represented by a random variable, here denoted as y
The statistical model proposed here can be applied in a wide variety of analyses where the standard deviations of Gaussian measurements are deemed to have a given relative uncertainty, reflected by the parameters ri defined in Eq (9)
The quadratic constraint terms connecting control measurements to their corresponding nuisance parameters that appear in the log-likelihood are replaced by logarithmic terms [cf
Summary
Data analysis in Particle Physics is based on observation of a set of numbers that can be represented by a (vector) random variable, here denoted as y. The quadratic constraint terms in Eq (3) correspond to the case where the estimate ui of the parameter θi is modeled as a Gaussian distributed variable of known standard deviation σui. The parameter θi could represent a not-yet computed coefficient in a perturbation series, and ui is one’s best guess of its value (e.g., zero) In this case one may try to estimate an appropriate σui by means of some recipe, e.g., by varying some aspects of the approximation technique used to arrive at ui. In the case of prediction based on perturbation theory one may try varying the renormalization scale in some reasonable range In such a case the estimate of σui results from fairly arbitrary choices, and values that may differ by. 50% or even a factor of two might not be unreasonable
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
