Third edition of Artificial Intelligence: foundations of computational agents, Cambridge University Press, 2023 is now available (including the full text).

### 6.5.5 Time Granularity

One of the problems with the definition of an HMM or a dynamic belief network is that the model depends on the time granularity. The time granularity can either be fixed, for example each day or each thirtieth of a second, or it can be event-based, where a time step exists when something interesting occurs. If the time granularity were to change, for example from daily to hourly, the conditional probabilities must be changed.

One way to model the dynamics independently of the time granularity is to model, for each variable and each value for the variable,

- how long the variable is expected to keep that value and
- what value it will transition to when its value changes.

Given a discretization of time, and a time model for state transitions, such as an exponential decay, the dynamic belief network can be constructed from this information. If the discretization of time is fine enough, ignoring multiple value transitions in each time step will only result in a small error. See Exercise 6.12.