A Bayesian framework is proposed to define flexible coupling models for joint decompositions of data sets. Under this framework, a solution to the joint decomposition can be cast in terms of a maximum a posteriori estimator. Examples of joint posterior distributions are provided , including general Gaussian priors and non Gaussian coupling priors. Then simulations are reported and show the effectiveness of this approach to fuse information from data sets, which are inherently of different size due to different time resolution of the measurement devices.