Estimating the selection efficiency

TL;DR

This paper reviews statistical methods, including Bayesian and Frequentist techniques, for accurately estimating event selection efficiency in experimental data analysis, addressing complex practical scenarios and prior selection issues.

Contribution

It provides a comprehensive comparison of Bayesian and Frequentist methods for efficiency estimation and introduces analytical solutions using Beta distributions for complex cases.

Findings

Bayesian approach yields analytical efficiency estimates.

Comparison of Frequentist and Bayesian methods.

Practical solutions for complex efficiency problems.

Abstract

The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist and Bayesian approaches are illustrated, and the problem of choosing a meaningful prior is explicitly addressed. Several practical use cases are considered, from the problem of combining different samples to complex situations in which non-unit weights or non-independent selections have been used. The Bayesian approach allows to find analytical expressions which solve even the most complicate problems, which make use of the family of Beta distributions, the conjugate priors for the binomial sampling.