How to measure efficiency

The measurement of the efficiency of some selection or process is always an important part of the analysis of experimental data. The statistical techniques needed to determine the efficiency and its uncertainty are reviewed, based on the use of the Bayes’ theorem. Uniform and non-uniform priors are considered in two real-life examples. The use of the uncertainties in practical cases is also considered, together with the problem of combining different samples. “Pathological” cases are also addressed, in which non-unit weights or non-independent selections have been used to fill the histograms. The use of the family of Beta distributions is illustrated in the examples, making use of its conjungate property for binomial sampling (if the prior belongs to such family, the posterior is also a Beta distribution). Finally, we recommend to specify the Beta parameters of prior and posterior as the best way of communicating efficiencies.