Estimating the selection efficiency

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.

💡 Research Summary

The paper provides a comprehensive statistical treatment of the problem of estimating selection efficiency, a quantity that is central to virtually every analysis of experimental data in high‑energy physics, astrophysics, and related fields. The authors begin by framing the efficiency ε as the probability that a given event passes a set of selection criteria. Under the simplest assumption of independent trials, the number of selected events k out of a total of n follows a binomial distribution, and the frequentist point estimator is the maximum‑likelihood value ε̂ = k/n. The authors review the standard frequentist confidence‑interval constructions: the normal approximation (σ≈√