The paper deals with Bayesian identification of time variant normal regression models and provides four key algorithms. The first two algorithms are designed for the online regularized identification of a single regression model. Absence of the time evolution model is solved in both algorithmizations by a data-informed forgetting technique. The choice of the forgetting factor in the first algorithm is performed using Variational Bayesian approximation. The second algorithm determines the value of the forgetting factor by statistical decision making.

The second pair of algorithms treats the problem of time evolution of parameters as a sequence of switching normal regression models. In both of these offline algorithms which are based on the Variational Bayesian approximation, both the inference of the bank of model parameters and the activities of these models over the time of the experiment are iteratively performed. The actual number of models forming this bank is determined automatically. The difference between these algorithms lies mainly in the noise properties of the switched models.

All four algorithms are tested on a real system and in simulations. The paper is complemented by a short introduction to the Bayesian world, which presents the essential statistical techniques that are used. For completeness and continuity with the aforementioned algorithms, the offline and online identification of a time invariant normal regression model is also described.