As discussed above in the context of introducing the Markov property, the feedback loops present in many natural systems suggest the need to include cycles in BNs. However, cycles can often be avoided by defining variables to represent long-term equilibrium values, rather short-term responses. When this is not reasonable, variables can be replicated or indexed to represent multiple points in time, so that the value of a variable at one time point can depend on the value at another, rather than having to refer back to itself (Figure 8). Such a model is referred to as a 'dynamic' (or 'temporal') BN and is a generalization of the familiar hidden Markov model and linear dynamical systems.
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