Reformulation of a likelihood approach to fake-lepton estimation in the framework of Bayesian inference

Prompt isolated leptons are essential in many analyses in high-energy particle physics but are subject to fake lepton background, i.e. objects that mimic the lepton signature. The fake-lepton background is difficult to estimate from simulation and is often directly determined from data. A popular method is the matrix method, which however suffers from several limitations. This paper recapitulates an alternative approach based on a likelihood with Poisson constraints and reformulates the problem from a different starting point in the framework of Bayesian statistics. The equality of both approaches is shown and several cases are studied in which the matrix method is limited. In addition, the fake-lepton background is recalculated and compared to the estimate with the matrix method in an example top-quark measurement.