We present an adaptation technique for statistical machine translation, which applies the well-known Bayesian learning paradigm for adapting the model parameters. Since state-of-the-art statistical machine translation systems model the translation process as a log-linear combination of simpler models, we present the formal derivation of how to apply such paradigm to the weights of the log-linear combination. We show empirical results in which a small amount of adaptation data is able to improve both the non-adapted system and a system which optimises the abovementioned weights on the adaptation set only, while gaining both in reliability and speed.