The authors show the connection of the initial enlargement to the concepts of “dynamical Bayesian modelling”. They recall how some initial enlargement results can be obtained using the so-called Girsanov approach. In this approach, the extra information is viewed as a statistical parameter and by defining a suitable statistical experiment one can find a semimartingale decomposition of a semimartingale in a bigger filtration. Examples related to Brownian filtration and to Poisson filtration are presented.