Estimating the selection efficiency

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.

References in corpus (6)

• Matching NLO QCD computations and parton shower simulations
• ROOT - A C++ Framework for Petabyte Data Storage, Statistical Analysis and Visualization
• The formal definition of reference priors
• Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process
• Frequentist Evaluation of Intervals Estimated for a Binomial Parameter and for the Ratio of Poisson Means
• Reference analysis of the signal + background model in counting experiments

Cited by in corpus (7)

• A NECTAr-based upgrade for the Cherenkov cameras of the H.E.S.S. 12-meter telescopes
• TARGET 5: a new multi-channel digitizer with triggering capabilities for gamma-ray atmospheric Cherenkov telescopes
• Combined sensitivity of JUNO and KM3NeT/ORCA to the neutrino mass ordering
• Neutron emission in ultraperipheral Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
• Track reconstruction and matching between emulsion and silicon pixel detectors for the SHiP-charm experiment
• Data reduction for a calorimetrically measured ${}^{163}\mathrm{Ho}$ spectrum of the ECHo-1k experiment
• Objective Bayesian analysis of counting experiments with correlated sources of background