  We present a novel scheme to combine neural machine translation (NMT) with
traditional statistical machine translation (SMT). Our approach borrows ideas
from linearised lattice minimum Bayes-risk decoding for SMT. The NMT score is
combined with the Bayes-risk of the translation according the SMT lattice. This
makes our approach much more flexible than $n$-best list or lattice rescoring
as the neural decoder is not restricted to the SMT search space. We show an
efficient and simple way to integrate risk estimation into the NMT decoder
which is suitable for word-level as well as subword-unit-level NMT. We test our
method on English-German and Japanese-English and report significant gains over
lattice rescoring on several data sets for both single and ensembled NMT. The
MBR decoder produces entirely new hypotheses far beyond simply rescoring the
SMT search space or fixing UNKs in the NMT output.
