  In this article, we present a method to calculate a posteriori event weights
at next-to-leading-order (NLO) QCD accuracy for a given jet event defined by
the (anti-)$k_t$ algorithm relying on the conventional $2\to 1$ recombination.
This is an important extension compared to existing Monte-Carlo tools which
generate jet events together with the corresponding weight but do not allow one
to calculate the weight for a given event. The method can be used to generate
unweighted events distributed according to the fixed-order NLO cross section.
In addition, the method allows one to calculate NLO accurate weights for events
recorded by experiments. The potential of this ability is illustrated by
applying the Matrix Element Method (MEM) to single top-quark events generated
with POWHEG in combination with Pythia. For the first time, a systematic study
of parton shower effects within the MEM is provided. The method is completely
general and can be applied to arbitrary LHC processes.
