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Biomedical problems are highly complex and multi-dimensional. Typically, only a small part of the relevant variables/data can be modelled by virtue of mechanistic modelling, since it hampered by the lack of the exact knowledge of the involved phenomena (C2). Typical non-modellable variables are -omics data, since the underlying regulatory networks dynamics are largely unknown and their coupling with higher scales is also non trivial (C3). Mechanistic models are great in analyzing the qualitative dynamic behavior of the system but rarely provide quantitative accurate predictions. On the other hand, statistical/machine learning methods are well-suited for quantitative reproduction the total observed data but they do not allow for a mechanistic understanding of the investigated problem. To overcome the afore-mentioned difficulties, I propose a grey-box methodogy that combines mechanistic modelling and machine learning. The idea is to develop a mechanistic model of the modellable variables that will serve an intelligent prior knowledge for the true function of system observables. In turn, this prior will be integrated in a Bayesian framework along with the non-modellable data. As a consequence, the resulting posterior is expected to be an improved observable prediction, due to the contribution of the non-modellable data on the mechanistic predictions. The underlying assumption of the method is that the correlations of the unmodellable data (e.g. genomic data) do not change too much in time. This method can be generalized to any type of non-modellable variables.