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This paper concerns the Bayesian tracking of slowly varying parameters of a linear stochastic regression model. The modelled and predicted system output is assumed to possess time-varying mean value, whereas its dynamics are relatively stable. The proposed estimation method models the system output mean value by time-varying offset. It formulates three extreme hypotheses on model parameters' variability: (i) no parameter varies; (ii) all parameters vary; and (iii) the offset varies. The Bayesian paradigm then provides a mixture as posterior distribution, which is appropriately projected to a feasible class. Exponential forgetting at 'second' hypotheses level allows tracking of slow variations of respective hypotheses.The developed technique is an example of a general procedure called partial forgetting. Focus on a simple example allows to demonstrate essence of the approach. Moreover, it is important per se as it corresponds with a varying load of otherwise (almost) time-invariant dynamic system.

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