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.