(eng): The big data, characterized by high volume, velocity and variety, often arise in a dynamic way, requiring fast online processing. This contribution proposes a new information-theoretic method for parallel dynamic statistical modelling of such data with a network of cooperating processing units and an optional fusion center. The concept strongly exploits the principles of the Bayesian information processing, allowing its abstract formulation for arbitrary distributions. As a particular case, we specialize to the popular exponential family posterior distributions, arising either directly or indirectly from modelling with generalized linear models. Still, the applicability is considerably wider.