Nonstationary environment. (A) The generative model. At each time point there is a probability for a change in the environment. When there is a change in the environment, that is, , the parameter is drawn from its prior distribution , independent of its previous value. Otherwise the value of retains its value from the previous time step . Given a parameter value , the observation is drawn from a probability distribution . We indicate random variables by capital letters, and values by lowercase letters. (B) Example of a nonstationary environment. Your friend meets you every day at the coffee shop (blue dot) starting after work from her office (orange dot) and crossing a river. The time of arrival of your friend is the observed variable , which due to the traffic or your friend's workload may exhibit some variability but has a stable expectation (). If, however, a new bridge is opened ( where is the moment of change), your friend no longer needs to take a detour. There is, then, a sudden change in her observed daily arrival times.
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