  Analyses in high energy physics aim to put the Standard Model---the commonly
accepted theory---to test. For convincing conclusions, analysis methods are
needed which offer an unambiguous comparison between data and theory while
allowing reliable estimates of uncertainties. The Matrix Element Method (MEM)
is a Maximum Likelihood method which is especially tailored for signal searches
and parameter estimation at colliders. The MEM has proven to be beneficial due
to optimal use of the available information and a clean statistical
interpretation of the results. But it has a big drawback: In its original
formulation, the likelihood calculation is intrinsically limited to the leading
perturbative order in the coupling. Higher-order corrections improve the
accuracy of theoretical predictions and allow for unambiguous field-theoretical
interpretation of the extracted information. In this work, the MEM
incorporating corrections of next-to-leading order (NLO) in QCD by defining
event weights suited for the likelihood calculation is presented for the first
time. These weights also enable the generation of unweighted events following
the cross section calculated at NLO accuracy. The method is demonstrated for
top-quark events. The top-quark mass is determined with the MEM at NLO accuracy
from the generated events. The extracted estimators are in agreement with the
input values from the event generation. Repeating the mass determinations from
the same events, without NLO corrections in the predictions, results in biased
estimators. These shifts may not be accounted for by estimated theoretical
uncertainties rendering the estimation of the theoretical uncertainties
unreliable in the leading-order analysis. The results emphasise the importance
of the inclusion of NLO corrections into the MEM.
