Bayesian system identification

In Bayesian statistics the concept of probability is interpreted as a rational measure of belief which is used to describe mathematically the uncertain relation between the statistician and the external world. The statistical inference is understood as a correction of prior subjective probability distribution by objective data. The paper shows that on this Bayesian basis it is possible to build a consistent theory of system identification. The following problems are considered: one-shot and real-time identification, estimation and prediction in closed control loop, redundant and unidentifiable parameters, time-varying parameters and adaptivity.