  Single top-quark production offers a unique laboratory for precision tests of
the Standard Model and searches of possible extensions. Furthermore, assuming
the Standard Model, single top-quark production can be used to determine
top-quark related couplings. For precise determinations of parameters like the
electroweak gauge couplings or the mass of the top quark, efficient, unbiased,
and theoretically unambiguous analysis methods are needed. Within this context,
the Matrix Element Method (MEM) has been established in hadron collider
analyses due to its possibility to top out at utilising the information
available in experimental data. However, so far it has mostly been applied in
Born approximation only. We discuss the extension to next-to-leading order
(NLO) accuracy. As a necessary prerequisite we introduce an efficient method to
calculate NLO QCD weights for jet events. As proof of concept and
representative example we use the MEM at NLO to reproduce the top-quark mass in
a toy experiment where we treat single top-quark events generated at NLO
accuracy as pseudo-data. This is the first application of the MEM at NLO
accuracy to the hadronic production of jets originating from coloured final
state partons. We observe that analysing NLO events with Born likelihoods can
introduce a pronounced bias in the extracted mass which would require
significant calibration with associated uncertainties. Although we focus on
parameter determinations, the methods presented here can also be used to search
for new physics using likelihood ratios.
