  Maximum a posteriori decoding, a commonly used method for neural machine
translation (NMT), aims to maximize the estimated posterior probability.
However, high estimated probability does not always lead to high translation
quality. Minimum Bayes Risk (MBR) decoding offers an alternative by seeking
hypotheses with the highest expected utility.
  In this work, we show that Quality Estimation (QE) reranking, which uses a QE
model as a reranker, can be viewed as a variant of MBR. Inspired by this, we
propose source-based MBR (sMBR) decoding, a novel approach that utilizes
synthetic sources generated by backward translation as ``support hypotheses''
and a reference-free quality estimation metric as the utility function, marking
the first work to solely use sources in MBR decoding. Experiments show that
sMBR significantly outperforms QE reranking and is competitive with standard
MBR decoding. Furthermore, sMBR calls the utility function fewer times compared
to MBR. Our findings suggest that sMBR is a promising approach for high-quality
NMT decoding.
