  Many high-energy physics analyses require the presence of leptons from $W$,
$Z$, or $H$ boson decay. For these analyses, signatures that mimic such leptons
present a `fake lepton' background that must be estimated. Since the magnitude
of this background depends strongly upon details of the detector response, it
can be difficult to estimate with simulation. One data-driven approach is the
`matrix method', in which two categories of leptons are defined (`loose' and
`tight'), with the tight category being a subset of the loose category. Using
the populations of leptons in each category in the analysis sample, and the
efficiencies for both real and fake leptons in the loose category to satisfy
the criteria for the tight category, the fake background yield can be
estimated. This paper describes a Poisson likelihood implementation of the
matrix method, which provides a more precise, reliable, and robust estimate of
the fake background yield compared to an analytic solution. This implementation
also provides a reliable estimate of the background for cases in which the
analysis selection permits more loose leptons than tight leptons, potentially
allowing for greater selection efficiency.

High Energy Physics - Experiment